Question

write the coordinates of the vertices after a reflection over the line $y = 6$.
$d(\square,\square)$
$e(\square,\square)$
$f(\square,\square)$
$g(\square,\square)$

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex:

• \( D(-4, 3) \) (since it's at x=-4, y=3)
• \( E(-4, 6) \) (x=-4, y=6)
• \( F(0, 6) \) (x=0, y=6)
• \( G(0, 3) \) (x=0, y=3)

Step2: Reflect over \( y = 6 \)

The formula for reflecting a point \( (x, y) \) over the horizontal line \( y = k \) is \( (x, 2k - y) \). Here, \( k = 6 \), so the new y - coordinate is \( 2(6)-y=12 - y \), and the x - coordinate remains the same.

For \( D(-4, 3) \):

New y - coordinate: \( 12-3 = 9 \), so \( D'(-4, 9) \)

For \( E(-4, 6) \):

New y - coordinate: \( 12 - 6=6 \), so \( E'(-4, 6) \)

For \( F(0, 6) \):

New y - coordinate: \( 12 - 6 = 6 \), so \( F'(0, 6) \)

For \( G(0, 3) \):

New y - coordinate: \( 12-3 = 9 \), so \( G'(0, 9) \)

Answer:

\( D'(-4, 9) \), \( E'(-4, 6) \), \( F'(0, 6) \), \( G'(0, 9) \)