Question

What is the reflection image of P(0, 0) after two reflections, first across x = 4 and then across y = -3?

Answer 1

Across x = 4 -> (8,0)

Across y = -3 -> (8,-6)

Answer 2

The reflection image of P(0, 0) after two reflections is P'(8,-6).

Explanation:

The given point is (0,0).

If a point reflect across x = 4, then

`(x,y)\rightarrow (-x+8,y)`

`(0,0)\rightarrow (-0+8,0)`

`(0,0)\rightarrow (8,0)`

If a point reflect across y = -3, then

`(x,y)\rightarrow (x,-y-6)`

`(8,0)\rightarrow (8,-0-6)`

`(8,0)\rightarrow (8,-6)`

Therefore the reflection image of P(0, 0) after two reflections is P'(8,-6).