Respuesta :
Answer:
The equation of hypotenuse is [tex]y=\frac{2}{3}(x)[/tex].
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 [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The hypotenuse passes through A(3,2) and C'(9,6) So, the equation of hypotenuse is
[tex]y-2=\frac{6-2}{9-3}(x-3)[/tex]
[tex]y-2=\frac{2}{3}(x-3)[/tex]
[tex]y-2=\frac{2}{3}(x)-2[/tex]
Add 2 on both sides.
[tex]y=\frac{2}{3}(x)[/tex]
Therefore, the equation of hypotenuse is [tex]y=\frac{2}{3}(x)[/tex].
