Find the coordinates of the vertices after a rotation 180 degrees about the origin. Screen Shot 2019-07-23 at 8.37.15 PM.png

Answer 1

R_{0, 180} (x, y) →(-x,-y) so that after a 180^ο rotation about (0,0)

(-3,2) →(3,-2)

(9,4) →(-9,-4)

Alternately, we can use slope to visualize it in the coordinate plane : the slope of the segment connecting center of rotation (0,0) with point (9,4) to be rotated is

4/9 and is ⊥ to segment with slope -9/4 ( a 90⁰ rotation) which is also ⊥ to -4/-9 (a second 90⁰ rotation) and gives final coordinates (-9,-4).

Answer 2

(x, y) → (-x, -y)

Examples: (2, 3) → (-2, -3)

(-1, 4) → (1, -4)

(5, 0) → (-5, 0)