Question

write the coordinates of the vertices after a reflection over the y-axis.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex.

• Point \( C \): From the graph, it's at \( (-10, -2) \).
• Point \( D \): At \( (0, -2) \).
• Point \( E \): At \( (0, 8) \).
• Point \( F \): At \( (-10, 8) \).

Step2: Apply reflection over y - axis rule

The rule for reflecting a point \( (x, y) \) over the \( y \)-axis is \( (x, y) \to (-x, y) \).

• For \( C(-10, -2) \): Apply the rule, \( x=-10 \) becomes \( -(-10) = 10 \), so \( C'=(10, -2) \).
• For \( D(0, -2) \): \( x = 0 \), so \( -0 = 0 \), thus \( D'=(0, -2) \).
• For \( E(0, 8) \): \( x = 0 \), so \( -0 = 0 \), thus \( E'=(0, 8) \).
• For \( F(-10, 8) \): \( x=-10 \) becomes \( -(-10)=10 \), so \( F'=(10, 8) \).

Answer:

\( C'(10, -2) \)
\( D'(0, -2) \)
\( E'(0, 8) \)
\( F'(10, 8) \)