Question

graph the image of rectangle pqrs after a reflection over the line y = 1.

Explanation:

Step1: Find coordinates of rectangle PQRS

Assume \( P(-9,-7) \), \( Q(-8,-7) \), \( R(-8,-9) \), \( S(-9,-9) \) (based on grid - point estimation).

Step2: Use reflection formula over \( y = c \)

The formula for reflecting a point \((x,y)\) over the line \( y = c \) is \((x,2c - y)\). Here \( c = 1 \), so the formula becomes \((x,2\times1 - y)=(x,2 - y)\).

• For \( P(-9,-7) \): \( x=-9,y = - 7 \), new \( y=2-(-7)=9 \), so \( P'(-9,9) \).
• For \( Q(-8,-7) \): \( x=-8,y = - 7 \), new \( y=2-(-7)=9 \), so \( Q'(-8,9) \).
• For \( R(-8,-9) \): \( x=-8,y = - 9 \), new \( y=2-(-9)=11 \), so \( R'(-8,11) \).
• For \( S(-9,-9) \): \( x=-9,y = - 9 \), new \( y=2-(-9)=11 \), so \( S'(-9,11) \).

Step3: Plot the new points

Plot \( P'(-9,9) \), \( Q'(-8,9) \), \( R'(-8,11) \), \( S'(-9,11) \) and connect them to form the reflected rectangle.

Answer:

Plot the points \( P'(-9,9) \), \( Q'(-8,9) \), \( R'(-8,11) \), \( S'(-9,11) \) and connect them to get the reflected rectangle.