Question

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

Answer 1

Answer:

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.