Question

write the coordinates of the vertices after a reflection over the line x = 5.
b((□, □))
c((□, □))
d((□, □))
e((□, □))

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex from the graph:

• \( B(3, -9) \)
• \( C(3, -5) \)
• \( D(4, -3) \)
• \( E(4, -7) \)

Step2: Reflection over \( x = 5 \)

The formula for reflecting a point \( (x, y) \) over the vertical line \( x = a \) is \( (2a - x, y) \). Here, \( a = 5 \), so the new \( x \)-coordinate is \( 2(5) - x = 10 - x \), and the \( y \)-coordinate remains the same.

For \( B(3, -9) \):

New \( x \)-coordinate: \( 10 - 3 = 7 \)
New \( y \)-coordinate: \( -9 \)
So, \( B'(7, -9) \)

For \( C(3, -5) \):

New \( x \)-coordinate: \( 10 - 3 = 7 \)
New \( y \)-coordinate: \( -5 \)
So, \( C'(7, -5) \)

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

New \( x \)-coordinate: \( 10 - 4 = 6 \)
New \( y \)-coordinate: \( -3 \)
So, \( D'(6, -3) \)

For \( E(4, -7) \):

New \( x \)-coordinate: \( 10 - 4 = 6 \)
New \( y \)-coordinate: \( -7 \)
So, \( E'(6, -7) \)

Answer:

\( B'(7, -9) \)
\( C'(7, -5) \)
\( D'(6, -3) \)
\( E'(6, -7) \)