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.

• \( Q \) is at \( (-9, -7) \) (since it's 9 units left on x - axis and 7 units down on y - axis).
• \( R \) is at \( (-9, -1) \) (9 units left on x - axis and 1 unit down on y - axis).
• \( S \) is at \( (-4, -4) \) (4 units left on x - axis and 4 units down on y - axis).

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:

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