Question

write the coordinates of the vertices after a translation 3 units left and 10 units down.

Explanation:

Step1: Find original coordinates

From the graph:

• \( R(-7, 1) \)
• \( U(-6, 1) \)
• \( S(-7, 10) \)
• \( T(-6, 10) \)

Step2: Apply translation (left 3, down 10)

Translation rule: \((x, y) \to (x - 3, y - 10)\)

• For \( R(-7, 1) \):

\( x' = -7 - 3 = -10 \), \( y' = 1 - 10 = -9 \) → \( R'(-10, -9) \)

• For \( U(-6, 1) \):

\( x' = -6 - 3 = -9 \), \( y' = 1 - 10 = -9 \) → \( U'(-9, -9) \)

• For \( S(-7, 10) \):

\( x' = -7 - 3 = -10 \), \( y' = 10 - 10 = 0 \) → \( S'(-10, 0) \)

• For \( T(-6, 10) \):

\( x' = -6 - 3 = -9 \), \( y' = 10 - 10 = 0 \) → \( T'(-9, 0) \)

Answer:

\( R'(-10, -9) \), \( U'(-9, -9) \), \( S'(-10, 0) \), \( T'(-9, 0) \)