Question

write the coordinates of the vertices after a reflection over the line x = -4.

Explanation:

Step1: Find the original coordinates

The original coordinates are \( W(-9,0) \), \( V(-7,3) \), \( U(-6,0) \), \( T(-7,-3) \).

Step2: Use the reflection formula over \( x = a \)

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

• For \( W(-9,0) \):

\( 2\times(-4)-(-9)=-8 + 9=1 \), so the new coordinate is \( (1,0) \).

• For \( V(-7,3) \):

\( 2\times(-4)-(-7)=-8 + 7=-1 \), so the new coordinate is \( (-1,3) \).

• For \( U(-6,0) \):

\( 2\times(-4)-(-6)=-8 + 6=-2 \), so the new coordinate is \( (-2,0) \).

• For \( T(-7,-3) \):

\( 2\times(-4)-(-7)=-8 + 7=-1 \), so the new coordinate is \( (-1,-3) \).

Answer:

The coordinates of the vertices after reflection are \( W'(1,0) \), \( V'(-1,3) \), \( U'(-2,0) \), \( T'(-1,-3) \).