Question

write the coordinates of the vertices after a translation 8 units right and 1 unit down.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex from the graph:

• \( Q(-6, -3) \)
• \( T(-6, -2) \)
• \( S(-2, -2) \)
• \( R(-2, -3) \)

Step2: Apply translation rules

For a translation 8 units right (add 8 to the \( x \)-coordinate) and 1 unit down (subtract 1 from the \( y \)-coordinate), use the transformation \( (x + 8, y - 1) \):

• For \( Q(-6, -3) \):

New \( x \): \( -6 + 8 = 2 \)
New \( y \): \( -3 - 1 = -4 \)
So \( Q' = (2, -4) \)

• For \( T(-6, -2) \):

New \( x \): \( -6 + 8 = 2 \)
New \( y \): \( -2 - 1 = -3 \)
So \( T' = (2, -3) \)

• For \( S(-2, -2) \):

New \( x \): \( -2 + 8 = 6 \)
New \( y \): \( -2 - 1 = -3 \)
So \( S' = (6, -3) \)

• For \( R(-2, -3) \):

New \( x \): \( -2 + 8 = 6 \)
New \( y \): \( -3 - 1 = -4 \)
So \( R' = (6, -4) \)

Answer:

The coordinates of the vertices after translation are \( Q'(2, -4) \), \( T'(2, -3) \), \( S'(6, -3) \), and \( R'(6, -4) \).