Question

What set of reflections would carry triangle ABC onto itself?

a. y-axis, x-axis, y-axis, x-axis
b. x-axis, y=x, y-axis, x-axis
c. x-axis, y-axis, x-axis
d. y=x, x-axis, x-axis

Answer 1

y-axis, x-axis, y-axis, x-axis

Answer 2

Answer: option a. y-axis, x-axis, y-axis, x-axis.

Justification:

1) start with an hypothetical point with general coordinates (a,b)

2) reflecting (a,b) over the y-axis translates it to (-a,b)

3) reflecting (-a,b) over the x-axis translates it to (-a,-b)

4) reflecting (-a,-b) over the y-axis translates it to (a,-b)

5) reflecting (a,-b) over the x-axis translated it to (a,b).

We have proven that that set of reflections carry any point onto itself and so the triangle ABC onto itself.