it’s in Greek :/

[oblique harness]

You might need to translate

Or

@lean berry

Eh

@naive whale

[runic briar]

Bro could you provide a translation of the problem

[celest sphinx]

α)prove that κ=2.
β) find the equation of the median AM of the triangle ΑΒΓ
γ) find the equation of the height ΓΔ of the triangle ΑΒΓ
δ) find the coordinates of the intersection point of the median AM and the height ΓΔ

α) write the coordinates of the points Α, Β, Γ
β)find the slope of the side ΑΓ
γ)find the equation of the side ΑΓ
δ)show that the triangle is right
ε)find the midpoint M of the side ΑΓ
στ) find the length of the median ΒΜ

13. Μ is the midpoint of ΑΒ
    α) find the coordinates of B
    β) find the equation of AB
    γ) if the length of the median ΓΜ of the triangle is √26 find the possible values of β
    δ)If Γ(-4,3) show that the triangle ΑΒΓ is isosceles

[runic briar]

Gonna repost image so I don’t have to scroll all the way back and forth translation to image

11
a) We know that the triangle is right, meaning the sum of the squares of the shorter leg’s lengths = square of long side’s length
To get the length of each leg we can simply use the distance formula
AL (using L for that symbol): sqrt((k+1)^2 + (5-k)^2)
BL: sqrt((8-k)^2 + (8-k)^2)
AB (hypotenuse or long side) : sqrt(9^2 + 3^2)
AL^2 + BL^2 = AB^2
(k+1)^2 + (5-k)^2 + (8-k)^2 • 2 = 90
Solve for k

11b) The median of a line is the line joining an angle and the bisector (halfway point) of the opposite side
In this case the angle is A so the opposite side is BL

1. Find the halfway point, or midpoint of BL, which is what M is
   2)Find the equation of the line that crosses thru A and M

11y) A height of a triangle is 90 degrees, or perpendicular to the base of the triangle. In this case, since L is the corner of the height, AB is the base.
Find a line perpendicular to line AB that crosses L

11S) Once you solve 11B and 11Y, simply find their intersection point

[runic briar]

Distance formula: Given points (a,b) and (c,d) the distance between them is sqrt((a-c)^2 + (b-d)^2)

[runic briar]

For this, it would best to use the midpoint formula
Given points A = (a,b) and B = (c,d) the midpoint of AB is ((a+c)/2,(b+d)/2)

[runic briar]

Given a line y=mx + b, where m is slope, a line perpendicular to it should have the slope -1/m, so a line perpendicular to y=2x + 5 would have a slope of -1/2

Question 12

A) Look at where each point is in the coordinates grid
B) Given two points (a,b) and (c,d) the slope between them is (d-b)/(c-a)
Y) Given a slope of a line m and a point on the line (a,b), you can do b=am + c, solve for c to get y-intercept
S) Find the length of all three sides using the distance formula from question 11A, and see if the sum of the square of the two smaller sides equals the square of the large side

e) Use midpoint formula

ot) Find midpoint of AL (should have already found in 12e) and find the line that goes thru M and B

Note: To find a line between two points, first find slope using slope formula and then find y-intercept with either point

13a) Use midpoint formula to find what the x and y value of B needs to be
13b) You should know how to do this by now
13y) Use distance formula to solve for B
13s) An isosceles triangle is one where two side lengths are equal. Find all the side lengths and show that two are equal

@blissful ocean these hints should hopefully help make the questions easier. Feel free to ping me if you need clarification on any problem, but try as much as you can to find the answer yourself, you will only learn if you do it yourself

[fiery lava]

@reef halo has given 1 rep to @runic briar

[runic briar]

Yea?

[lapis aspen]

+close