Question

write the coordinates of the vertices after a reflection over the line x = -4. k((□, □)) l((□, □)) m((□, □)) n((□, □))

Explanation:

Step1: Find original coordinates

First, identify original coordinates:

• \( K(-9, -2) \), \( L(-6, -2) \), \( M(-6, 3) \), \( N(-9, 3) \).

Step2: Reflection formula over \( x = a \)

The formula for reflecting a point \( (x, y) \) over \( x = a \) is \( (2a - x, y) \). Here, \( a = -4 \), so the new \( x \)-coordinate is \( 2(-4) - x = -8 - x \), and \( y \)-coordinate remains.

Step3: Reflect \( K \)

For \( K(-9, -2) \):
\( x' = -8 - (-9) = 1 \), \( y' = -2 \). So \( K'(1, -2) \).

Step4: Reflect \( L \)

For \( L(-6, -2) \):
\( x' = -8 - (-6) = -2 \), \( y' = -2 \). So \( L'(-2, -2) \).

Step5: Reflect \( M \)

For \( M(-6, 3) \):
\( x' = -8 - (-6) = -2 \), \( y' = 3 \). So \( M'(-2, 3) \).

Step6: Reflect \( N \)

For \( N(-9, 3) \):
\( x' = -8 - (-9) = 1 \), \( y' = 3 \). So \( N'(1, 3) \).

Answer:

\( K'(1, -2) \)
\( L'(-2, -2) \)
\( M'(-2, 3) \)
\( N'(1, 3) \)