this is quite difficult for me
#i need help with this question!
wraith garnet
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this is quite difficult for me
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delicate oriole
this is quite difficult for me
Since triangles AOB and BO'C are similar, we have AO/BO' = AB/BC.
You can find AO by finding the x-intercept of the line.
Next, the triangle OBC has base OB, which can be found from the y-intercept of the line, and height BO', which can be found from the formula above.
wraith garnet
Since triangles AOB and BO'C are similar, we have AO/BO' = AB/BC.
You can find A...
ok thanks i am trying to do the first steps and i got x intercept as (-12/5, 0) is that correct
versed summitBOT
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delicate oriole
ok thanks i am trying to do the first steps and i got x intercept as (-12/5, 0) ...
Yes.
wraith garnet
ok thanks and is y intercept coordinate (0,4)?
delicate oriole
Yes.
delicate oriole
No need for coordinates. Use the property of similar triangles that I wrote above.
wraith garnet
oh ok but dont i need it to find the length of BC so i can find the area?
delicate oriole
No, not really.
As I said, triangle BOC has base BO and height BO', which is all you need.
wraith garnet
Oh ok i am slightly confused at the moment
does that mean that AOB and OBC are similar
delicate oriole
No, AOB and BO'C are.
wraith garnet
ohhh
ok i drew that what is the next step?
i have coordinates of A and B as well
delicate oriole
Well, if you've proven that AOB and BO'C are similar, then we have AO/BO' = AB/BC. From here you can find BO'.
delicate oriole
must i do pythagoras to find AB length?
No. Find BO' from the proportion.
You know that AO = 12/5 and AB/BC = 2/7.
So, you can find BO'.
wraith garnet
would BO' be 3.5x AO?
delicate oriole
Yes.
wraith garnet
Ok thanks
ok so far i have got this:
AO/BO'=AB/BC
AB/BC=2/7
and AO/BO'=(12/5)/BO'
so (12/5)/BO' = 2/7
2(BO')/7=12/5
2(BO')=84/5
so BO' =42/5
is that right?
delicate oriole
Yeah, BO' = 42/5.
wraith garnet
that is good
delicate oriole
So, now you know that BO' = 42/5 and BO = 4. So, you can now find the area of OBC.
wraith garnet
now i must find CO' right
delicate oriole
No, there is no need.
wraith garnet
oh wat will be the height then since BO is my base
delicate oriole
oh wat will be the height then since BO is my base
No. The height needs to be perpendicular to the base. So, the height is BO', as it's perpendicular to the base BO.
delicate oriole
Yes.
wraith garnet
is triangle OBO' the same as triangle OBC?
delicate oriole
Well, they aren't the same triangle, but their areas are the same.
delicate oriole
They both have the same base (BO) and height (BO'), so their areas are the same.
delicate oriole
You're welcome! Now you just need to find the area of OBC.
wraith garnet
i think i got it is it 84/5?
delicate oriole
Yeah.
wraith garnet
ok thanks
i think i understand it no
now
but its just confusing how OBC and OBO' have same area but i understand how now
btw which side of triangle OBC has the same length as height (BO')
delicate oriole
btw which side of triangle OBC has the same length as height (BO')
None. It isn't a right triangle, so its height doesn't coincide with any of its sides.