Question

write the coordinates of the vertices after a reflection over the line x = -6.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of \( P \), \( Q \), and \( R \) from the graph.

• \( P \) is at \( (-6, -8) \) (since it's on \( x = -6 \), \( y = -8 \)).
• \( Q \) is at \( (-6, -3) \) (on \( x = -6 \), \( y = -3 \)).
• \( R \) is at \( (-9, -9) \) (from the grid, \( x = -9 \), \( y = -9 \)).

Step2: Reflect over \( x = -6 \)

The formula for reflecting a point \( (x, y) \) over the vertical line \( x = a \) is \( (2a - x, y) \). Here, \( a = -6 \), so the reflection formula becomes \( (2(-6) - x, y) = (-12 - x, y) \).

For \( P(-6, -8) \):

Substitute \( x = -6 \) into the reflection formula:
\( x' = -12 - (-6) = -12 + 6 = -6 \)
\( y' = -8 \)
So \( P'(-6, -8) \).

For \( Q(-6, -3) \):

Substitute \( x = -6 \) into the reflection formula:
\( x' = -12 - (-6) = -6 \)
\( y' = -3 \)
So \( Q'(-6, -3) \).

For \( R(-9, -9) \):

Substitute \( x = -9 \) into the reflection formula:
\( x' = -12 - (-9) = -12 + 9 = -3 \)
\( y' = -9 \)
So \( R'(-3, -9) \).

Answer:

\( P'(-6, -8) \)
\( Q'(-6, -3) \)
\( R'(-3, -9) \)