Question

write the coordinates of the vertices after a translation 8 units down.

Explanation:

Step1: Identify original coordinates

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

• \( A \): \( (-6, 0) \)
• \( B \): \( (0, 0) \)
• \( C \): \( (-4, 4) \)

Step2: Apply translation (8 units down)

A translation 8 units down subtracts 8 from the \( y \)-coordinate of each vertex. The translation rule is \( (x, y) \to (x, y - 8) \).

• For \( A(-6, 0) \):

New \( y \)-coordinate: \( 0 - 8 = -8 \)
New coordinates: \( (-6, -8) \)

• For \( B(0, 0) \):

New \( y \)-coordinate: \( 0 - 8 = -8 \)
New coordinates: \( (0, -8) \)

• For \( C(-4, 4) \):

New \( y \)-coordinate: \( 4 - 8 = -4 \)
New coordinates: \( (-4, -4) \)

Answer:

• \( A' \): \( (-6, -8) \)
• \( B' \): \( (0, -8) \)
• \( C' \): \( (-4, -4) \)