Question

write the coordinates of the vertices after a reflection over the line x = -4.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex:

• \( T(-8, -3) \)
• \( U(-6, 0) \)
• \( V(-8, 3) \)
• \( W(-10, 0) \)

Step2: Reflection over \( x = -4 \)

The formula for reflecting a point \( (x, y) \) over the vertical line \( x = a \) is \( (2a - x, y) \). Here, \( a = -4 \), so the new \( x \)-coordinate is \( 2(-4) - x = -8 - x \), and the \( y \)-coordinate remains the same.

For \( T(-8, -3) \):

New \( x \)-coordinate: \( -8 - (-8) = 0 \), \( y \)-coordinate: \( -3 \). So \( T'(0, -3) \).

For \( U(-6, 0) \):

New \( x \)-coordinate: \( -8 - (-6) = -2 \), \( y \)-coordinate: \( 0 \). So \( U'(-2, 0) \).

For \( V(-8, 3) \):

New \( x \)-coordinate: \( -8 - (-8) = 0 \), \( y \)-coordinate: \( 3 \). So \( V'(0, 3) \).

For \( W(-10, 0) \):

New \( x \)-coordinate: \( -8 - (-10) = 2 \), \( y \)-coordinate: \( 0 \). So \( W'(2, 0) \).

Answer:

\( T'(0, -3) \)
\( U'(-2, 0) \)
\( V'(0, 3) \)
\( W'(2, 0) \)