Question

write the coordinates of the vertices after a reflection over the line ( y = 2 ).

Explanation:

Step1: Find the coordinates of \( Q, R, S \)

From the graph, \( Q(-4,4) \), \( R(-4,10) \), \( S(0,2) \).

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

The formula for reflecting a point \( (x,y) \) over the line \( y = c \) is \( (x,2c - y) \). Here \( c = 2 \), so the formula becomes \( (x,4 - y) \).

For \( Q(-4,4) \):

Substitute \( x=-4,y = 4 \) into \( (x,4 - y) \).
\( x=-4 \), \( 4-y=4 - 4=0 \). So \( Q'(-4,0) \).

For \( R(-4,10) \):

Substitute \( x=-4,y = 10 \) into \( (x,4 - y) \).
\( x=-4 \), \( 4-y=4-10=-6 \). So \( R'(-4,-6) \).

For \( S(0,2) \):

Substitute \( x = 0,y = 2 \) into \( (x,4 - y) \).
\( x=0 \), \( 4-y=4 - 2=2 \). So \( S'(0,2) \).

Answer:

\( Q'(-4,0) \), \( R'(-4,-6) \), \( S'(0,2) \)