Question

write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex:

• \( S(-9, 1) \) (since it's at x=-9, y=1)
• \( T(-9, 10) \) (x=-9, y=10)
• \( U(-1, 6) \) (x=-1, y=6)
• \( V(-1, 3) \) (x=-1, y=3)

Step2: Apply 180° rotation rule

The rule for a 180° counterclockwise (or clockwise) rotation around the origin is \((x, y) \to (-x, -y)\).

For \( S(-9, 1) \):

Apply the rule: \( (-(-9), -1) = (9, -1) \)

For \( T(-9, 10) \):

Apply the rule: \( (-(-9), -10) = (9, -10) \)

For \( U(-1, 6) \):

Apply the rule: \( (-(-1), -6) = (1, -6) \)

For \( V(-1, 3) \):

Apply the rule: \( (-(-1), -3) = (1, -3) \)

Answer:

• \( S' (9, -1) \)
• \( T' (9, -10) \)
• \( U' (1, -6) \)
• \( V' (1, -3) \)