Question

write the coordinates of the vertices after a reflection over the x-axis. e(□,□) f(□,□) g(□,□)

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points \( E \), \( F \), and \( G \) from the graph.

• For point \( E \): Looking at the grid, it is at \( (1, -3) \) (since it's 1 unit right on the x - axis and 3 units down on the y - axis).
• For point \( F \): It is at \( (2, -3) \) (2 units right on the x - axis and 3 units down on the y - axis).
• For point \( G \): It is at \( (2, -7) \) (2 units right on the x - axis and 7 units down on the y - axis).

Step2: Apply reflection over x - axis rule

The rule for reflecting a point \( (x,y) \) over the \( x \) - axis is \( (x, -y) \). This means we keep the \( x \) - coordinate the same and change the sign of the \( y \) - coordinate.

• For \( E(1, - 3) \): Applying the rule, \( E'=(1, -(-3))=(1,3) \).
• For \( F(2, - 3) \): Applying the rule, \( F'=(2, -(-3))=(2,3) \).
• For \( G(2, - 7) \): Applying the rule, \( G'=(2, -(-7))=(2,7) \).

Answer:

\( E'(1, 3) \)
\( F'(2, 3) \)
\( G'(2, 7) \)