Question

graph the image of kite qrst after a reflection over the y-axis.

Explanation:

Step1: Find Coordinates of Vertices

First, identify the coordinates of each vertex of kite QRST.

• \( Q(-6, -3) \)
• \( R(-2, -2) \)
• \( S(-6, 0) \)
• \( T(-10, -2) \)

Step2: Apply Reflection Over y - axis

The rule for reflecting a point \((x, y)\) over the \( y \)-axis is \((x, y) \to (-x, y)\).

• For \( Q(-6, -3) \): New coordinate \( Q'(6, -3) \) (since \(-(-6)=6\), \( y \)-coordinate remains \(-3\))
• For \( R(-2, -2) \): New coordinate \( R'(2, -2) \) (since \(-(-2)=2\), \( y \)-coordinate remains \(-2\))
• For \( S(-6, 0) \): New coordinate \( S'(6, 0) \) (since \(-(-6)=6\), \( y \)-coordinate remains \(0\))
• For \( T(-10, -2) \): New coordinate \( T'(10, -2) \) (since \(-(-10)=10\), \( y \)-coordinate remains \(-2\))

Step3: Plot the New Vertices

Plot the points \( Q'(6, -3) \), \( R'(2, -2) \), \( S'(6, 0) \), and \( T'(10, -2) \) on the coordinate plane and connect them to form the reflected kite.

Answer:

The reflected kite \( Q'R'S'T' \) has vertices at \( Q'(6, -3) \), \( R'(2, -2) \), \( S'(6, 0) \), and \( T'(10, -2) \) (plotted on the coordinate plane as described).