Question

write the coordinates of the vertices after a translation 2 units left and 2 units up.
u((
v(
w(

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of \( U \), \( V \), and \( W \) from the graph.

• \( U \) is at \( (2, 0) \)
• \( V \) is at \( (2, 3) \)
• \( W \) is at \( (-3, 3) \)

Step2: Apply translation rules

A translation 2 units left means subtract 2 from the \( x \)-coordinate, and 2 units up means add 2 to the \( y \)-coordinate. The translation rule is \( (x, y) \to (x - 2, y + 2) \).

For \( U' \):

Substitute \( x = 2 \), \( y = 0 \) into the rule:
\( x' = 2 - 2 = 0 \), \( y' = 0 + 2 = 2 \). So \( U'(0, 2) \).

For \( V' \):

Substitute \( x = 2 \), \( y = 3 \) into the rule:
\( x' = 2 - 2 = 0 \), \( y' = 3 + 2 = 5 \). So \( V'(0, 5) \).

For \( W' \):

Substitute \( x = -3 \), \( y = 3 \) into the rule:
\( x' = -3 - 2 = -5 \), \( y' = 3 + 2 = 5 \). So \( W'(-5, 5) \).

Answer:

\( U'(0, 2) \)
\( V'(0, 5) \)
\( W'(-5, 5) \)