Mathematics: 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 :

Find the image of a (-6, 5) after two reflections,

bm42400

10.03.2022

a. A'(-6,-15)

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

Step-by-step 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.

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