Question

Find the image of A (-6, 5) after two reflections, first across the line y = -5, then across the

line x = -12. Write your answer for both reflections or show your graph with each step. (2
points)
a. Reflection 1: y = -5 :
b. Reflection 2: x = -12 :

Answer 1

a.
`A'(-6,-15)`

b.
`A''(-18,-15)`

Explanation:

The given point is
`A(-6,5)`.

We want to find the image after this point has been reflected in the line
`y=-5`.

Recall that, the mapping for a reflection in the line
`y=k` is

`P(x,y)\rightarrow P'(x,2k-y)`.

This implies that,

`A(-6,5)\rightarrow A'(-6,2(-5)-5)`.

This simplifies to,

`A(-6,5)\rightarrow A'(-6,-10-5)`.

This will finally give us,

`A(-6,5)\rightarrow A'(-6,-15)`.

b. We now apply the second reflection, which is a reflection in the line
`x=-12`.

Recall again that, the reflection in the line
`x=k` has the mapping

`P(x,y)\rightarrow P'(2k-x,y)`.

This implies that,

`A'(-6,-15)\rightarrow A''(2(-12)--6,-15)`.

This implies that,

`A'(-6,-15)\rightarrow A''(-24+6,-15)`.

This will finally give us,

`A'(-6,-15)\rightarrow A''(-18,-15)`.

See graph in attachment.