Question

write the coordinates of the vertices after a reflection over the line y = -6.

Explanation:

Step1: Find original coordinates

From the graph, \( A(1, -2) \), \( B(5, -2) \), \( C(-1, -5) \).

Step2: Reflection over \( y = k \) formula

The formula for reflecting a point \( (x, y) \) over the line \( y = k \) is \( (x, 2k - y) \). Here, \( k = -6 \), so the formula becomes \( (x, 2(-6) - y)=(x, -12 - y) \).

Step3: Reflect point A

For \( A(1, -2) \): \( x = 1 \), \( y = -2 \). New \( y \)-coordinate: \( -12 - (-2)= -12 + 2 = -10 \). So \( A'(1, -10) \).

Step4: Reflect point B

For \( B(5, -2) \): \( x = 5 \), \( y = -2 \). New \( y \)-coordinate: \( -12 - (-2)= -10 \). So \( B'(5, -10) \).

Step5: Reflect point C

For \( C(-1, -5) \): \( x = -1 \), \( y = -5 \). New \( y \)-coordinate: \( -12 - (-5)= -12 + 5 = -7 \). So \( C'(-1, -7) \).

Answer:

\( A'(1, -10) \)
\( B'(5, -10) \)
\( C'(-1, -7) \)