Question

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

Answer 1

first reflect across x=-3

you get (-6,0)

then reflect across y=4

we have (-6,8)

x=-6

y=8

Answer 2

The reflection image would be (-6,8).

Explanation:

Since, when a point is reflected across a line x = p

Then, the rule of reflection is,

`(x,y)\rightarrow (2p-x, y)`

While, across a line y = p,

The rule of reflection is,

`(x,y)\rightarrow (x, 2p-y)`

Thus, when (0,0) is reflected across x = -3,

`(0,0)\rightarrow (2(-3)-0,0)`

The image after reflection is (-6,0),

Again when (-6,0) is reflected across y = 4,

`(-6,0)\rightarrow (-6, 2(4)-0)`

Hence, the resultant image after both reflections would be (-6,8).