is this better
#linear-algebra
wintry steppe
the sum of the areas of the triangles appears to be 44
narrow mortar
YES
THATS WHAT THE CALCULATOR HAD
LOL
the one i used
and i sent u it
I HAVE TRIANGLEPHOBEIA NOW
IM SCARED OF TRIANGLES
wintry steppe
right
but that's the wrong way to get the calculation
like you got the answer out of pure coincidence
half ice
Well then you're not scared of this shape because it's not a triangle
wintry steppe
^^^^
narrow mortar
yay
wintry steppe
there is no answer to a wrong question
narrow mortar
DUDE
wintry steppe
idk why you keep asking for an answer
narrow mortar
BUT I DONT WANNA FAIL
wintry steppe
when we've been trying to tell you that the question is wrong
pale coyote
ugh whats the confusion, the problem makes no sense just tell the teacher that
wintry steppe
send the diagram that I've given you to the teacher
narrow mortar
"OH WHY DONT U MAKE MY LESSON PLANS"
pale coyote
how can you fail, tell them theyre wrong and if they take points off file a complaint
wintry steppe
and tell him that the question is wrong
narrow mortar
they know im dumb lol
wintry steppe
and if he penalizes you, then raise it with his department chair or something
wintry steppe
bruh it's not about being dumb
narrow mortar
tho im actually not dumg
pale coyote
lol oh boy
wintry steppe
and that diagram will convince any competent mathematician that he's wrong
narrow mortar
hes gonna be like how u do that
wintry steppe
he's not
he's not that incompetent
he'll realize his mistake
send the diagram
along with a note that
pale coyote
your teacher is just very careless or doesnt know what theyre doing or both
wintry steppe
"b and c are not parallel"
narrow mortar
lol
wintry steppe
and he will instantly see his mistake
it's a very simple mistake to understand
you're just making this far more difficult than it has to be
wintry steppe
send that along with a short note that "b and c are not parallel"
dusky epoch
what are y'all even doing at this point
narrow mortar
ok
ima be like
my heads gonna explode b and c are not parallel
explode head emoji
wintry steppe
just send the diagram and "b and c are not parallel" and if he goes "you're wrong," send it to his boss
narrow mortar
lol
wintry steppe
no don't ask him whether it's correct
wintry steppe
just tell him straightforward
that it's not a triangle because "b and c are not parallel"
and send the diagram
he's not going to argue when he's obviously wrong
limber sierra
i was thinking the vectors were rotated somehow or some shit, but if the question requires rotating vectors
lmao
and even then, that'd require for the right angle to
not actually be right
narrow mortar
?
narrow mortar
yes?
wintry steppe
please
dusky epoch
what is going on
i cannot tell
wintry steppe
limber sierra
ann
someone asks a question which asks to calculate the
"area of a triangle formed by the vectors"
and then it lists vector numbers but
the vectors literally cant form a triangle
as the diagram describes
dusky epoch
limber sierra
wintry steppe
make sure he can see the entirety of the diagram you've drawn
and send that
straight up
wintry steppe
maybe add a note "it's not a triangle"
pale coyote
Sir
narrow mortar
ok
wintry steppe
he can't hate you for being right
pale coyote
poopies
wintry steppe
the sum of the areas of the triangles appears to be 44
@wintry steppe wait, thats what i said a couple hours ago
someone told me it was wrong
dusky epoch
are you sure you wanna send that in with that spelling
pale coyote
lol
wintry steppe
and that grammar^
dusky epoch
that too.
wintry steppe
u sound very sassy in this
@wintry steppe no, it's a mere coincidence that the sum of the areas is 44 and that the area of the triangle given by those 3 points is 44
dusky epoch
whatever
narrow mortar
me sound sassy?
wintry steppe
yes u should^
narrow mortar
SHE @pale coyote
wintry steppe
if its professional email, u should care
narrow mortar
lol
oh ok
how should I write it
also i have sent him stupid emails so um
lol
coz im funny
wintry steppe
"Sir, the vectors b and c are not parallel, so the figure in the question cannot be a triangle. I hope that the diagram that I've attached makes this clear."
by parallel do u mean in the same span?
that one is a scalar multiple of the other
or that one is in the span of the other
wintry steppe
that diagram is drawn incorrectly
narrow mortar
lol
wintry steppe
just don't worry about it and send the diagram and email
you're making it far harder than it is
no, show them the better graph
wintry steppe
"Sir, the vectors b and c are not parallel, so the figure in the question cannot be a triangle. I hope that the diagram that I've attached makes this clear."
narrow mortar
hello sir when i graphed it i was not getting the same diagram as u. A and b are not parallel.
pale coyote
@kind sky_@
narrow mortar
that sounds nice^
wintry steppe
u can win + shift + s to screen shot
and ctrl + v to paste it
pale coyote
im losing it
wintry steppe
how
narrow mortar
hello sir when i graphed it i was not getting the same diagram as u. A and b are not parallel.
wintry steppe
okay, I'm not going to argue with you
I think I've given you a reasonable solution to your problem and explained it
narrow mortar
sorry plz no
pale coyote
yea this is insane
wintry steppe
why are u scared when u are on the right side
he's not going to retaliate if he's clearly made a mistake
pale coyote
jesus christ
wintry steppe
scroll up
rough schooner
are we allowed to post hw questions here related to linear algebra?
narrow mortar
"Sir, the vectors b and c are not parallel, so the figure in the question cannot be a triangle. I hope that the diagram that I've attached makes this clear."
ok the last sentence sounds rude lol
pale coyote
just send him a chat log of this whole thing
pale coyote
jesus what the fuck
narrow mortar
trying to talk to me like that LOL
pale coyote
whatsup @rough schooner
rough schooner
wintry steppe
Then do something like
Sir, the vectors b and c are not parallel, so the figure in the question cannot be a triangle. I've drawn and attached a diagram of the figure.
"Sir, the vectors b and c are not parallel, so the figure in the question cannot be a triangle. Could this be a mistake?"
pale coyote
so what does it mean to be a subspace?
rough schooner
sorry i feel like im interuptting a conversation...
wintry steppe
@rough schooner you're not
pale coyote
no, its welcomed lol
wintry steppe
dw about it
pale coyote
so you have a checklist a candidate set needs to pass for it to be a subspace
what are the things on the checklist
rough schooner
1.must be a 0 vector
pale coyote
contain the 0 vector*
pale coyote
do you fully understand these conditions?
wintry steppe
do you know what closed under addition means?
rough schooner
nope but like i've seen an example problem and thats as far as my understanding goes
wintry steppe
@narrow mortar make sure u can see the whole graph
or theres no point of the email
pale coyote
so in all your examples your sets are defined by a property that elements satisfy to be in that set
narrow mortar
ye it is seen
pale coyote
you need to check that if x and y are in the set to start with (they both satisfy the given property), does x + y also satisfy that property?
rough schooner
uhh what
pale coyote
3x3 matrices, all entries integers
rough schooner
where are you getting x+y from
pale coyote
thats what closure under addition means
take two elements of the set, call them x and y, and check if x + y is also in the set
rough schooner
okay so what im confused on tho in this problem there's not really a given matrix
pale coyote
for example: If S is the set of odd integers, is this closed under addition?
rough schooner
i would assume so
pale coyote
take two odd numbers x and y, is x + y odd?
rough schooner
nope
pale coyote
so is S closed under addition
narrow mortar
done its sent the email
pale coyote
to prove its not closed under addition you can give a concrete counterexample
rough schooner
just so that im understanding you correctly that means it doesn't meet the condtion, right?
rough schooner
got it
pale coyote
the 'condition' is 'being odd'
narrow mortar
OK IMA SLEEP BRAINCELLS HAVE DIED
pale coyote
in your first problem the 'condition/requirement' to be in the set is that all the matrix entries are integers
first check, if A and B are matrices of all integers, is A + B as well?
rough schooner
yes
pale coyote
okay if A is a matrix of all integers, and c is any real nubmer
number
is cA a matrix of all integers?
rough schooner
no
rough schooner
1/3 times 1
rough schooner
uhh what?
limber sierra
1 is a number, not a matrix.
pale coyote
1/3 times 1 is not a valid counterexample, youre trying to prove stuff about 3x3 matrices of integers
rough schooner
1/3 times a matrix with integers will not lead to integers...
pale coyote
your intuition is right but you need to be a little more precise
yeah but you gotta convince me
give me a full counterexample so im convinced
give me a specific 3x3 matrix
rough schooner
1/3 times [1 2 3] = [1/3 2/3 1] which does not satisfy the req condition?
pale coyote
[1,2,3] is not a 3x3 matrix.
rough schooner
idk how to format a matix on my computer...
pale coyote
just describe the matrix in words then
rough schooner
okie
pale coyote
or write the rows [a,b,c], [c,d,e], [e,f,g]
rough schooner
a 3x3 matrix with R1 [1. 2, 3] R2 [1,2,3] R3[1,2,3] multiplied by a constant of 1/3 does not satisfy the req condition
rough schooner
cool
pale coyote
so it is not a subspace
rough schooner
weirdly writing that out is helping me soldify the def
pale coyote
this is more or less basically how every subspace proof goes, but sometimes a shortcut is if you can immediately tell if 0 is not in the given set
rough schooner
uhh what do you mean
pale coyote
is the set of vectors in R^3 that take the form [1, x, y] for x and y real numbers a subspace?
rough schooner
no
pale coyote
you could go through and check closure under addition and scalar multiplication
rough schooner
or im assuming..
pale coyote
but you see that immediately [0,0,0] is not of this form, so it is not in that set, so it is not a subspace because subspaces must contain the 0 vector
hollow finch
It also fails both closure under addition and scalar mult
pale coyote
you would hav ealso seen this if you tried closer under scalar/addition
so when in doubt just check those two things
rough schooner
ooo got it
pale coyote
try for part b then
rough schooner
okay
shrewd mortar
it is an affine space though
rough schooner
i think b is not a subspace
dusky epoch
can i see the original question again
pale coyote
why?
dusky epoch
is it more "here are some sets, determine if they're subspaces"
rough schooner
yup
pale coyote
yeah thats all it is Ann
rough schooner
yes
pale coyote
why do you think that @rough schooner did you check closure?
rough schooner
dusky epoch
and we're talking about B, yes?
pale coyote
ah you dont have to actually write anything, just check them off ?
dusky epoch
icyblue, do you remember what we did yesterday?
rough schooner
i know that it meets the addtion and scalar condtion
rough schooner
uhhh that not my actual answer
rough schooner
i know it isnt a subspace because of the third condition for the first one
pale coyote
is that a boys surface
rough schooner
but for the second it meets the scalar and addition condition but idk how to go about the first condition
pale coyote
whats the first condition
rough schooner
the zero vector is the first condition
dusky epoch
@summer sand this channel is occupied, please move.
summer sand
where do i go?
dusky epoch
summer sand
thank you
pale coyote
if its closed under scalar multiplication, what happens if you multiply by 0?
also even easier here
rough schooner
turns to zero
pale coyote
the thing you wanna check is does the 0 matrix satisfy my condition?
so here does the 0 matrix have the last row all 0s?
rough schooner
uhh if im understanding that correctly then yes
pale coyote
yeah 0 matrix definitely has last row all 0s
so its part of your set of all things that have last row all 0s
so its in there and so we have a subspace
rough schooner
but what about the other two rows that have other numbers
pale coyote
they can be any numbers, the only thing you care about is if the last row is all 0s
rough schooner
oh okay so if any row is all 0s it automatically meets the first condition?
pale coyote
huh no thats the set youre defining
the set youre thinking about is the 3x3 matrices with last row all 0s
pale coyote
no, it depends how the set youre considering is defined
dusky epoch
your set is defined as the set of all matrices whose third row is all zeroes
as far as the membership of a matrix in this set goes you do not care about what its other two rows are
rough schooner
oh okay...
dusky epoch
just to help you not overthink it mb
pale coyote
youre a bouncer at the door of a club and youre checking if someones allowed in. Different sets are given by different conditions to be allowed in. For this set somethings allowed in if the last row is all 0s, thats all you care about.
pale coyote
it's very literal.
rough schooner
its just weird because i thought all of the matrix had to be 0 to meet the conditions because thats what i thought the definition was
pale coyote
nope.
dusky epoch
yes
rough schooner
cool
rough schooner
for the third one the only condition is that its the diagonal portion of the matrix
pale coyote
uhh the condition is that it is a diagonal matrix
dusky epoch
the condition is that everything off the diagonal is 0
as per the definition of a diagonal matrix
rough schooner
ohh
pale coyote
so the only place the matrix could be non-zero is on the main diagonal, everywhere else its 0
check to see if this set is closed under addition and scalar mult.
rough schooner
okay let me think this one through and get back to you
rough schooner
it would be a subspace
rough schooner
ugh finally im starting to process this
pale coyote
good!
rough schooner
what is a symmetric matrix
pale coyote
$A^T = A$
stoic pythonBOT
moonside:
rough schooner
t= transpose right?
pale coyote
yes
rough schooner
sorry my professor never goes any notations
pale coyote
kill them
dusky epoch
rough schooner
lol
pale coyote
dusky epoch
anyway yes a symmetric matrix is by definition a matrix equal to its own transpose
pale coyote
its sleepytime soon i thinks
rough schooner
so an identity matrix would work for that
pale coyote
sure.
dusky epoch
nope
rough schooner
oh damn
dusky epoch
the set of all invertible matrices doesn't even contain the zero matrix
bc the zero matrix is not invertible
so
yknow
rough schooner
oh what is that just part of the def?
dusky epoch
what no
okay let's put it this way
do you think the zero matrix is invertible
and if so, what do you think its inverse is
rough schooner
i thought so cause i think if you multiple anything with it itll just equal the same matrix
pale coyote
maybe i missed something
rough schooner
what?
dusky epoch
you seem to be mixing up the ZERO matrix and the IDENTITY matrix.
dusky epoch
the zero matrix is the matrix consisting of all zeroes
this matrix is very not invertible
rough schooner
ohhh i just looked up the definition of the invertible matrix
i did not have a clear understanding of it
okay cool
okay just to make sure my reasoning for d was correct
dusky epoch
you didn't provide much of it
what you said boiled down to "the identity matrix is in this set"
rough schooner
it is not a subspace cause if you multiply it with a neg it will not meet the req
dusky epoch
ok we're a bit all over the place
and this could be worded better
but yes that's correct for D
rough schooner
okay cool
pale coyote
ah you asked about symmetric matrices, but then went back to the one before it
rough schooner
yea i did my bad i should've clarified
rough schooner
Wait what i thought the dimension simply depended upon the subscript of the subspaces.....
dusky epoch
no
for one, the dimension of M_3(R) itself isn't 3
and that of M_5(R) itself isn't 5 either
pale coyote
wrong channel
rough schooner
what?
wintry steppe
oh mkay mb~
dusky epoch
i mean
dusky epoch
dimension is dimension. it is not "whatever number you pull out of the notation"
the dimension of a space is the number of elements in any of its bases
so you will need to find a basis for S
and then count how many elements there are in it
in both cases.
pale coyote
sleepytime
elfin ingot
rough schooner
The way i did this was i said 2 is an element of R
and x=1/2 as these meet the two conditions
and then i added these two values together to get a resulting answer of 5/2
therefore the interval is not a subspace of r2 as it is not closed under vector addition
however when i was double checking my answer using closed scalar multiplication using the same two values i get an answer of one which is part of the interval and so the interval is a subspace of r2
slow scroll
... why do you add 2 to 1/2 exactly?
rough schooner
is that one of the req for subspaces?
closure addition or something of that sorts
and i just picked 2 and 1/2 randomly
slow scroll
"2 is an element of R"
so what? If you want to show that subset is not closed under addition, you need to pick an example of two elements from that subset, add them together, and confirm that the answer you get lies outside the subset
slow scroll
2 is not an element of that subset?
rough schooner
what
slow scroll
these are ordered pairs of the form (x,y) where |x| <= 1 and y = 0
2 is not an ordered pair
rough schooner
oh okay so do i pick 1/2 is an element of r and thenx=0?
im a lil confused now...
slow scroll
(1,0) is an element for example. What other element could you choose to add to it, so that you get something that is not in the subset?
slow scroll
nope. (1.5, 0) is not in the subset, because 1.5 > 1
rough schooner
i don't think any number in the interval when added to zero will equal outside of the interval
slow scroll
hm? You just need to add something to (1,0) so that the first coordinate is greater than 1.
dusky epoch
(0.9, 0) is in your set
adding it to itself will result in (1.8, 0), which isn't in your set
therefore the set {(x,y) | -1 โค x โค 1, y = 0} FAILS to be closed under addition.
rough schooner
ohhh
dusky epoch
i can come up with more counterexamples if you wish
slow scroll
you can do the same thing with scalar multiplication too. they both fail
rough schooner
can you explain it in terms of the zero vector condition
slow scroll
2(1,0) = (2,0) and 2>1
rough schooner
i struggle with that
slow scroll
it contains the zero vector, so it passes there
dusky epoch
the zero vector condition is satisfied but in order to be a subspace your set needs to satisfy all three
slow scroll
since -1 <= 0 <= 1 and y=0 we have that (0,0) is in the subset
rough schooner
ohhh
thanks a lot!
Can someone explain how to go about this problem? I tried looking it up on chegg but i still don't understand these steps...
dusky epoch
they took two arbitrary elements of W (the subset they're checking for subspace-hood) and showed that an arbitrary linear combination of those two is still in W
which is equivalent to checking closure under addition and scaling
but like two in one
and it went without saying that W is nonempty
rough schooner
uhh what so is v and w separate vectors that they deduced from the conditions ?
dusky epoch
there are no lowercase v and lowercase w
V, uppercase V, is what they used to denote the ambient vector space. V here is the space of polynomials of degree at most 6.
W, uppercase W, is what they used to denote the subset of V that we want to check for subspace-hood.
W here is the set of polynomials of degree at most 3.
they showed that for any scalars a, b and any vectors ฮฑ, ฮฒ โ W, the linear combination aฮฑ + bฮฒ is still in W.
i'm trying my best here to, pardon my language, dumb this down.
rough schooner
is this the only way to go about this problem?
dusky epoch
no, but any other way will boil down to essentially the same thing.
all "determine if this is a subspace" questions are the same.
rough schooner
at the part where she is defining the two vectors V and W at the end they put a colon and then it says a0 times a1....a6 element of r, why exactly are they doing this ?
rough schooner
my bad
narrow mortar
@wintry steppe Dude he replied
"They donโt need to be. Work with what is there."
narrow mortar
@wintry steppe he said that lol
@dusky epoch I have a question if ur ok with that
I dont understand what my teacher meant he said
for that
which resultant triangle is he talking about?
@half ice
Can u explain what he meant?
im confused..
tender smelt
lol I'm also confused
What he meant is propably that the diagram shows vectors b and c as collinear, but from the assumptions we know b and c are not scalar multiples of each other
But I have no idea what the "given triangle" is if the three vectors don't form a triangle in that configuration
Unless it is supposed to mean "the triangle obtained by the starting points of the three vectors"
narrow mortar
he also said
"No the entire triangle that results when you sort out the vectors b and c. There is a third vector there that is unmarked you have to Think about the question ... that is why it is Thinking. "
@tender smelt
the actual triangle looks like
people told me yesterday
wintry steppe
@narrow mortar did you plot it? is that really what it looks like?
narrow mortar
ye someone helped me do that yesterday
but what do i have to find im so confused
he told me but im confused on what my teacher meant
@wintry steppe
wintry steppe
you don't know how to find the the height of a triangle?
narrow mortar
I dont know what Im even finding..
wintry steppe
you need the area
narrow mortar
which triangle?
tho
is he talking about
"The vectors are clearly not collinear, but you need to find that area of the resulting triangle nonetheless where the one side is obtained by using sides b and cNo the entire triangle that results when you sort out the vectors b and c. There is a third vector there that is unmarked you have to Think about the question ... that is why it is Thinking. "
wintry steppe
show me how you plotted it
narrow mortar
someone plotted it yesterday then i redrew it
wintry steppe
yes, ok
they're vectors
they start from the origin
and end at those coordinates
narrow mortar
yes
narrow mortar
ok
wintry steppe
so those are the coordinates for the tips of the triangle (i.e. vertices)
narrow mortar
oh
wintry steppe
have you tried splitting the triangle in horizontal/vertical parts
?
so that it's easier to find the height for each "mini-triangle"
wintry steppe
I don't know if the plotting is correct
I'll have to check
but do you understand what I mean by getting the height?
wintry steppe
how else are you gonna calculate the area of a triangle?
narrow mortar
which?
narrow mortar
wintry steppe
-1, 2
3, -8
5, 9
narrow mortar
there^
wintry steppe
ok
narrow mortar
so i have to find the area of that?
narrow mortar
oh
wintry steppe
narrow mortar
oh so the
wintry steppe
both form 90 degree angles there
narrow mortar
wbtw
the traingles
are not
right triangles
he made that clear
yesterday night -_-
wintry steppe
it's not a right triangle, no
narrow mortar
yes
wintry steppe
but you can split it
wintry steppe
narrow mortar
@half ice u there?
half ice
Dafuq why are we still talking about this broken question
It's not a triangle it has 4 sides lol
pale coyote
jesus christ still?
narrow mortar
lol
LOL
YES GUYS coz @wintry steppe asked me to email my teacher
coz the question made no sense and i asked
and told u what he said LOL
now i gotta do it ๐
pale coyote
are you in university or high school
wintry steppe
@half ice
this is how a vector is represented
do you agree?
except instead of OA, this question has it as just a
actually, now that I think about it... the vectors don't have to begin at the origin
you can move them around anywhere you want
half ice
What did he say? I missed it?
half ice
"No the entire triangle that results when you sort out the vectors b and c. There is a third vector there that is unmarked you have to Think about the question ... that is why it is Thinking. "
Did you tell him that what gets "sorted out" is not a triangle? Lol
wintry steppe
you can even give them labels:
wintry steppe
b + c = an edge for the triangle
wintry steppe
any way...
after plotting those point...
(drawing those vectors, sorry)
what are their magnitudes?
hint: ||Pythagoraaaaaaaaa||
then we'll assemble the triangle like in the diagram
are you guys with me so far?
narrow mortar
but
huh
oh
omg
so I can just find three triangles area
and then
add?
@wintry steppe
so like
wintry steppe
yep
narrow mortar
wintry steppe
you have to first find the magnitude of these vectors
(i.e. the length of the hypothenuse)
then replace the sides from here with those values:
wintry steppe
wintry steppe
you mean vector b or "b" as in "base"?
pale coyote
its not written that way though
wintry steppe
it's the same thing
pale coyote
he doesnt have magnitude of vectors, he has the vectors themselves
wintry steppe
@pale coyote https://cdn.discordapp.com/attachments/540211747613704221/710857028691558531/unknown.png
this is how you represent vectors
pale coyote
i know.
pale coyote
draw the three vectors, then try to arrange them so b and c form the base of a triangle
wintry steppe
narrow mortar
ok
pale coyote
you cant
pale coyote
ask your teacher if he meant the lengths of the triangle sides were equal to the magnitude of the indicated vectors?
pale coyote
yes
narrow mortar
ok
ripe dagger
how do i graph this in cartesian
half ice
Cry
wintry steppe
vectors*
pale coyote
do whatever you want im done talking about this
narrow mortar
oof..
ok ;-;
aww wow am I annoying u guys ๐ฆ
I dont wanna give up tho..
I find this very hard but ๐ฆ i wanna be able to do it
half ice
Star, the resulting figure is not a triangle. This is not "very hard", there is simply no acceptable answer
half ice
He doesn't seem to know haha
half ice
The third vector is the height
half ice
No, he's asking you to find the area of the literal triangle
narrow mortar
but he said
not the entire
triangle
by that he mean
the entire shape
i think he means one of the triangles
inside the shape
half ice
No, he's asking you to find the area of the literal triangle
half ice
He thinks that it can be found by using baseรheight. So, your job is to find the height
That's the third vector
narrow mortar
oh
wheres that
@half ice
@half ice Question would i just have to do this then
wintry steppe
a cleaner result would be to break down those radicals into something like 2โ75 or something
because they don't tell you to round off to two digits
wintry steppe
you could use the approximate values from the paranthesis
but I don't recommend it
narrow mortar
wow ok
wintry steppe
always keep results in fractions if you can
wintry steppe
where?
narrow mortar
u labelled b as a u switched
which is why i was confused before coz u end up getting a negative height
narrow mortar
lol ye
wintry steppe
lmao
narrow mortar
a= sqrt 5
b= sqrt 73
c= sqrt 106
btw he had also told me that
That side with b and c labelled is formed by the addition of those two vectors
so like
i have to find that?
half ice
Sorry I'm at work so I might disappear lol
narrow mortar
1/2 (|b-c|*|b-a|) be ok
thats what me and my friends did but we assumed right triangles? coz at night he posted they weren't but like none of us know how to do it at all
half ice
Your teacher expects |b| + |c| for the length of the base, and |b - a| for the height.
narrow mortar
oh so this is fine
wintry steppe
why b - a?
half ice
So the area is 1/2 (|b| + |c|)(|b - a|). Do that, you'll get full marks
wintry steppe
why is the height b-a?
narrow mortar
sorry kind blurry
half ice
But that's not going to calculate the actual area of whatever imaginary figure your teacher has concocted here
narrow mortar
lol
but sqrt 8497 would be ok?
thats what i had at first but everyones saying its wrong now
coz we assumed right triangles??
half ice
There's no right answer
narrow mortar
lol
wintry steppe
8497 seems like a lot
half ice
You can make any assumption you want and get something new. This is the simplest answer it could be perceived to be, and likely the one your teacher expects
narrow mortar
ye
wintry steppe
narrow mortar
whats the answer my teacher wants lol
narrow mortar
oh but
wintry steppe
I marked inside of parenthesis
narrow mortar
i subtracted their
coordinates
then found their
magnitude
and got sqrt (293)
narrow mortar
(3,-8) - (5,9)
wintry steppe
wintry steppe
the diagram has some arrows on it
wintry steppe
maybe if you put vector a to start from the same spot as vector b...
narrow mortar
what do u mean
wintry steppe
I mean like this:
vector a and b start from the same vertex on the diagram
(same point)
narrow mortar
hm
wintry steppe
and if you put vector c to match the arrows on the diagram...
the blue points are the "real" vertices of the triangle
narrow mortar
hm
wintry steppe
they match the arrows of the diagram
wintry steppe
you know both of the hypothenuses
and you can count the height
or you could just look at the coordinates for the middle vertex
vertex A and vertex C are not on the same line
narrow mortar
hmm
wintry steppe
can any of the angles be determined?
narrow mortar
uhh
wintry steppe
what is the slope of AB?
rise over run
for every 1 unit we go right, we drop 2 units down
wintry steppe
wait, hang on...
narrow mortar
can u rotate the diagram
wintry steppe
drops down 8 units while going 3
narrow mortar
question
wintry steppe
they're not on the same line
narrow mortar
to find the height
can i solve
CA
and get
the hyptenuse then
use Pythagorean ?
wintry steppe
CA is not a hypothenuse
wintry steppe
for any of the triangles
wintry steppe
hypothenuse is only for 90 degree triangles
wintry steppe
...
wintry steppe
this question is bullshit
wintry steppe
vector a and vector b are not on the same line, they form a vertex
wintry steppe
...which means that the overall shape is not a triangle
wintry steppe
maybe you're supposed to add vector a and vector b together
to form a new edge
because that's what you have when you add two vectors
narrow mortar
hm
wintry steppe
the diagram wants it to be an edge
stoic pythonBOT
narrow mortar
oh
lol
@wintry steppe
U KNOW WHAT IM THINKING!!
ok so u know how b and c are
gonna be the base
so then wont a and b be the other sides?
so the sides are a, b , (b-c) ?
wintry steppe
b and c are not the base
narrow mortar
then what is?
wintry steppe
it does indeed look like 2 triangles
if you follow the instructions from that diagram
half ice
So the way I gave you is definitely the intended method.
You can also find the left and right parts of the triangle separately. Note this will not give the same answer because this is not a triangle.
wintry steppe
you can still find the area of the shape, tho
half ice
Yes of course. Splitting it up gives the "real" area
narrow mortar
oh
so kaynex
it will be
A= (1/2)(|b-c|)(|b-a|)
@half ice
lol
@wintry steppe u there?
half ice
No, |b| + |c| would be the base
wintry steppe
yeah guys I used the question on a test
narrow mortar
LOL
wintry steppe
and everyone got my answer, so it must be right
narrow mortar
lol
wintry steppe
there are two triangles in the figure
half ice
Yeah agreed. It's really too simple. There's going to be people who do this the "wrong" way and get the wrong answer
narrow mortar
yes
wintry steppe
so he's just being stupid
narrow mortar
oh did u see what he said to me above?
wintry steppe
ask the head of the math department to find the area of the "given" triangle
narrow mortar
lol
wintry steppe
and include the diagram with two triangles in it
wintry steppe
I don't need to ask a math prof to know this is dumb