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

b

Explanation:

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Answer 2

The equation of hypotenuse is
`y=(2)/(3)(x)`.

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=(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=(6-2)/(9-3)(x-3)`

`y-2=(2)/(3)(x-3)`

`y-2=(2)/(3)(x)-2`

Add 2 on both sides.

`y=(2)/(3)(x)`

Therefore, the equation of hypotenuse is
`y=(2)/(3)(x)`.