Question

With the coordinates of the figure below after a rotation of 180° about the origin.

Answer 1

Rotation of 180° about the origin transforms point (x, y) into (-x, -y). Therefore:

A (3, 1) -> A' (-3, -1)

B (5, 4) -> B' (-5, -4)

C (7, 2) -> C' (-7, -2)

D (4, 0) -> D' (-4, 0)

Length of AD = √[(3 - 4)² + (1 - 0)²] = √2

Length of A'D' = √[(-3 - (-4))² + (-1 - 0)²] = √2