Question

graph the image of △uvw after a translation 12 units left and 2 units down.

Explanation:

Step1: Find coordinates of U, V, W

From the graph:

• \( U(3, 3) \) (since it's 3 units right on x, 3 up on y)
• \( V(5, 3) \) (5 right on x, 3 up on y)
• \( W(2, 9) \) (2 right on x, 9 up on y)

Step2: Apply translation (left 12, down 2)

Translation rule: \((x, y) \to (x - 12, y - 2)\)

• For \( U(3, 3) \):

\( x' = 3 - 12 = -9 \), \( y' = 3 - 2 = 1 \) → \( U'(-9, 1) \)

• For \( V(5, 3) \):

\( x' = 5 - 12 = -7 \), \( y' = 3 - 2 = 1 \) → \( V'(-7, 1) \)

• For \( W(2, 9) \):

\( x' = 2 - 12 = -10 \), \( y' = 9 - 2 = 7 \) → \( W'(-10, 7) \)

Step3: Plot the new points

Plot \( U'(-9, 1) \), \( V'(-7, 1) \), \( W'(-10, 7) \) and connect them to form the translated triangle.

Answer:

The translated triangle \( \triangle U'V'W' \) has vertices at \( U'(-9, 1) \), \( V'(-7, 1) \), and \( W'(-10, 7) \). (Graph by plotting these points and connecting them.)