Question

write the coordinates of the vertices after a reflection over the line x = -1.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex:

• \( Q(-9, -2) \)
• \( R(-9, 1) \)
• \( S(-1, 3) \)
• \( T(-1, 0) \)

Step2: Reflection over \( x = -1 \)

The formula for reflecting a point \( (x, y) \) over the line \( x = a \) is \( (2a - x, y) \). Here, \( a = -1 \), so the formula becomes \( (2(-1) - x, y) = (-2 - x, y) \).

For \( Q(-9, -2) \):

\( x' = -2 - (-9) = -2 + 9 = 7 \), \( y' = -2 \). So \( Q'(7, -2) \).

For \( R(-9, 1) \):

\( x' = -2 - (-9) = 7 \), \( y' = 1 \). So \( R'(7, 1) \).

For \( S(-1, 3) \):

\( x' = -2 - (-1) = -2 + 1 = -1 \), \( y' = 3 \). So \( S'(-1, 3) \) (since it's on the line of reflection, it doesn't change).

For \( T(-1, 0) \):

\( x' = -2 - (-1) = -1 \), \( y' = 0 \). So \( T'(-1, 0) \) (also on the line of reflection, no change).

Answer:

\( Q'(7, -2) \), \( R'(7, 1) \), \( S'(-1, 3) \), \( T'(-1, 0) \)