Question

write the coordinates of the vertices after a reflection over the y - axis.
q((□,□))
r((□,□))
s((□,□))

Explanation:

Step1: Find original coordinates

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

• For \( Q \): Looking at the grid, the \( x \)-coordinate is \(-9\) and the \( y \)-coordinate is \(-7\), so \( Q(-9, -7) \).
• For \( R \): The \( x \)-coordinate is \(-9\) and the \( y \)-coordinate is \(-1\), so \( R(-9, -1) \).
• For \( S \): The \( x \)-coordinate is \(-4\) and the \( y \)-coordinate is \(-4\), so \( S(-4, -4) \).

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 \( Q(-9, -7) \): Apply the rule: \( x=-9\to -(-9) = 9 \), \( y=-7\) remains. So \( Q'(9, -7) \).
• For \( R(-9, -1) \): Apply the rule: \( x = -9\to-(-9)=9 \), \( y=-1\) remains. So \( R'(9, -1) \).
• For \( S(-4, -4) \): Apply the rule: \( x=-4\to-(-4) = 4 \), \( y=-4\) remains. So \( S'(4, -4) \).

Answer:

\( Q'(9, -7) \)
\( R'(9, -1) \)
\( S'(4, -4) \)