Question

if the figure below were reflected across the x-axis, where would the points p, q, and r be? grid image p select q select r select

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points \( P \), \( Q \), and \( R \) from the graph.

• \( P \): From the grid, \( x = 3 \), \( y = 4 \), so \( P(3, 4) \).
• \( Q \): \( x = -2 \), \( y = 1 \), so \( Q(-2, 1) \).
• \( R \): \( x = 0 \), \( y = -5 \), so \( R(0, -5) \).

Step2: Apply reflection over x - axis

The rule for reflecting a point \( (x, y) \) across the \( x \)-axis is \( (x, -y) \) (the \( x \)-coordinate stays the same, the \( y \)-coordinate is negated).

• For \( P(3, 4) \):

Apply the rule: \( (3, -4) \), so \( P'(3, -4) \).

• For \( Q(-2, 1) \):

Apply the rule: \( (-2, -1) \), so \( Q'(-2, -1) \).

• For \( R(0, -5) \):

Apply the rule: \( (0, -(-5))=(0, 5) \), so \( R'(0, 5) \).

Answer:

\( P'(3, -4) \), \( Q'(-2, -1) \), \( R'(0, 5) \)