Given that δabc and δa'b'c' are similar right triangles that share the same slope, m, on the coordinate plane. find the equation in the form y = mx that represents the line of the hypotenuses if δabc has base coordinates of a = (3, 2) and b = (6, 2), and δa'b'c' has a height coordinates of b' = (9, 2) and c' = (9, 6).

The equation of hypotenuse is .

Step-by-step explanation:

It is given that ΔABC and ΔA'B'C' are similar right triangles that share the same slope, m, on the coordinate plane.

ΔABC has base coordinates of A = (3, 2) and B = (6, 2).

Base of ΔABC = AB

Base of ΔA'B'C' = A'B'

ΔA'B'C' has a height coordinates of B' = (9, 2) and C' = (9, 6)

Height of ΔABC = BC

Height  of ΔA'B'C' = B'C'

It means ∠B and ∠B' are right angles and points A, A', C, and C' lie on the hypotenuse.

If a line passes through two points and , then the equation of line is

The hypotenuse passes through A(3,2) and C'(9,6) So, the equation of hypotenuse is

Add 2 on both sides.

Therefore, the equation of hypotenuse is .