Question

note: it might be helpful to use patty paper to perform the transformation on graph paper.
translate the image:
reflect over the x axis
chart with a coordinate grid and a blue polygon labeled b, c, d, e
enter the coordinates of the new shape in the form (x, y) :
b is at
c is at
d is at
e is at

Explanation:

Step1: Identify original coordinates

First, we find the original coordinates of points \( B \), \( C \), \( D \), and \( E \) from the graph.

• \( B \): Looking at the graph, \( B \) is at \( (3, -8) \)
• \( C \): \( C \) is at \( (2, -6) \)
• \( D \): \( D \) is at \( (4, -4) \)
• \( E \): \( E \) is at \( (6, -7) \)

Step2: Apply reflection over x - axis rule

The rule for reflecting a point \( (x, y) \) over the \( x \) - axis is \( (x, -y) \). This is because reflecting over the \( x \) - axis changes the sign of the \( y \) - coordinate while keeping the \( x \) - coordinate the same.

• For point \( B(3, -8) \):

Using the reflection rule, the new \( y \) - coordinate is \( -(-8)=8 \), so \( B'=(3, 8) \)

• For point \( C(2, -6) \):

The new \( y \) - coordinate is \( -(-6) = 6 \), so \( C'=(2, 6) \)

• For point \( D(4, -4) \):

The new \( y \) - coordinate is \( -(-4)=4 \), so \( D'=(4, 4) \)

• For point \( E(6, -7) \):

The new \( y \) - coordinate is \( -(-7)=7 \), so \( E'=(6, 7) \)

Answer:

\( B' \) is at \( (3, 8) \)
\( C' \) is at \( (2, 6) \)
\( D' \) is at \( (4, 4) \)
\( E' \) is at \( (6, 7) \)