Question

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

Explanation:

Step1: Identify original coordinates

First, find the original coordinates of points \( E \), \( F \), and \( G \). From the graph:

• \( E \) is at \( (1, -3) \)
• \( F \) is at \( (2, -3) \)
• \( G \) is at \( (2, -7) \)

Step2: Apply reflection over x-axis

The rule for reflecting a point \( (x, y) \) over the x-axis is \( (x, -y) \). So we change the sign of the y-coordinate for each point.

For \( E(1, -3) \):
New y-coordinate: \( -(-3) = 3 \), so \( E' = (1, 3) \)

For \( F(2, -3) \):
New y-coordinate: \( -(-3) = 3 \), so \( F' = (2, 3) \)

For \( G(2, -7) \):
New y-coordinate: \( -(-7) = 7 \), so \( G' = (2, 7) \)

Answer:

The coordinates after reflection over the x - axis are \( E'(1, 3) \), \( F'(2, 3) \), \( G'(2, 7) \)