Question

Given triangle ABC with coordinates A(−5, 4), B(−5, 1), and C(−7, 0), and its image A′B′C′ with A′(−1, 0), B′(−4, 0), and C′(−5, −2), find the line of reflection.

The line of reflection is at y=?

Answer 1

y = x+5

Explanation:

Answer 2

y = x+5

Explanation:

A graph can help.

__

The line of reflection will pass through the midpoints of AA' and BB'.

The midpoint of AA' is ((-5, 4) +(-1, 0))/2 = (-3, 2)

The midpoint of BB' is ((-5, 1) +(-4, 0))/2 = (-4.5, 0.5)

The slope of the line through these points is ...

Δy/Δx = (2 -0.5)/(-3-(-4.5)) = 1.5/1.5 = 1

Then the y-intercept can be found from

y = x + b

2 = -3 + b

5 = b

So, the line of reflection is ...

y = x + 5