Question

In the diagram, points E, A, and B are collinear and the areas of square ABCD and right triangle EAD are equal. What are the coordinates of A?

A. (-7.5, 3)

B. (-8, 4)

C. (-9, 6)

D. (-8.5, 5)

E. (-6, 5)

Answer 1

(B) -8,4

Explanation:

Answer 2

(-8,4)

Explanation:

Given in the picture is a right triangle and a square sharing one commonside

Area of triangle = area of square

ie
`1/2 bs = s^2` (is s is one side of square)

i.e. b = 2s where b = EA

In other words A divides line EB in the ratio 2:1

Using section formula

Coordinates of A=

`((2(-7)+1(-10))/(3) ,(2(2)+1(-8))/(3))\\=(-8, 4)`