Question

graph the image of △stu after a translation 2 units right and 6 units down.

Explanation:

Step1: Find coordinates of T, S, U

From the graph:

• \( T(-8, 0) \)
• \( S(-8, -1) \)
• \( U(0, 1) \)

Step2: Apply translation (right 2, down 6)

Translation rule: \( (x, y) \to (x + 2, y - 6) \)

• For \( T(-8, 0) \):

\( x' = -8 + 2 = -6 \), \( y' = 0 - 6 = -6 \) → \( T'(-6, -6) \)

• For \( S(-8, -1) \):

\( x' = -8 + 2 = -6 \), \( y' = -1 - 6 = -7 \) → \( S'(-6, -7) \)

• For \( U(0, 1) \):

\( x' = 0 + 2 = 2 \), \( y' = 1 - 6 = -5 \) → \( U'(2, -5) \)

Step3: Plot \( T' \), \( S' \), \( U' \) and connect

Plot the new points \( T'(-6, -6) \), \( S'(-6, -7) \), \( U'(2, -5) \) on the coordinate plane and draw the triangle.

(Note: Since the task is to graph, the final answer involves plotting these points. The key is calculating the translated coordinates as shown.)

Answer:

Step1: Find coordinates of T, S, U

From the graph:

• \( T(-8, 0) \)
• \( S(-8, -1) \)
• \( U(0, 1) \)

Step2: Apply translation (right 2, down 6)

Translation rule: \( (x, y) \to (x + 2, y - 6) \)

• For \( T(-8, 0) \):

\( x' = -8 + 2 = -6 \), \( y' = 0 - 6 = -6 \) → \( T'(-6, -6) \)

• For \( S(-8, -1) \):

\( x' = -8 + 2 = -6 \), \( y' = -1 - 6 = -7 \) → \( S'(-6, -7) \)

• For \( U(0, 1) \):

\( x' = 0 + 2 = 2 \), \( y' = 1 - 6 = -5 \) → \( U'(2, -5) \)

Step3: Plot \( T' \), \( S' \), \( U' \) and connect

Plot the new points \( T'(-6, -6) \), \( S'(-6, -7) \), \( U'(2, -5) \) on the coordinate plane and draw the triangle.

(Note: Since the task is to graph, the final answer involves plotting these points. The key is calculating the translated coordinates as shown.)