Question

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).

Answer 1

Answer:

b

Step-by-step explanation:

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Answer 2

Answer:

The equation of hypotenuse is $y=\frac{2}{3}(x)$.

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 $(x_1,y_1)$ and $(x_2,y_2)$, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-2=\frac{6-2}{9-3}(x-3)$

$y-2=\frac{2}{3}(x-3)$

$y-2=\frac{2}{3}(x)-2$

Add 2 on both sides.

$y=\frac{2}{3}(x)$

Therefore, the equation of hypotenuse is $y=\frac{2}{3}(x)$.