Question

write the coordinates of the vertices after a reflection over the line y = -6. a(□,□) b(□,□) c(□,□)

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points \( A \), \( B \), and \( C \) from the graph.

• Point \( A \): \( (1, -2) \)
• Point \( B \): \( (5, -2) \)
• Point \( C \): \( (-1, -5) \)

Step2: Reflection over \( y = -6 \)

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

For point \( A(1, -2) \):

Substitute \( x = 1 \), \( y = -2 \) into the formula:
\( y' = -12 - (-2) = -12 + 2 = -10 \)
So, \( A' = (1, -10) \)

For point \( B(5, -2) \):

Substitute \( x = 5 \), \( y = -2 \) into the formula:
\( y' = -12 - (-2) = -10 \)
So, \( B' = (5, -10) \)

For point \( C(-1, -5) \):

Substitute \( x = -1 \), \( y = -5 \) into the formula:
\( y' = -12 - (-5) = -12 + 5 = -7 \)
So, \( C' = (-1, -7) \)

Answer:

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