Answer:
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
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
The hypotenuse passes through A(3,2) and C'(9,6) So, the equation of hypotenuse is
![y-2=\frac{6-2}{9-3}(x-3)](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7B6-2%7D%7B9-3%7D%28x-3%29)
![y-2=\frac{2}{3}(x-3)](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7B2%7D%7B3%7D%28x-3%29)
![y-2=\frac{2}{3}(x)-2](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7B2%7D%7B3%7D%28x%29-2)
Add 2 on both sides.
![y=\frac{2}{3}(x)](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%7D%7B3%7D%28x%29)
Therefore, the equation of hypotenuse is
.