Answer:
(x, y) right-arrow (negative x, negative y) ⇒ (x, y) → (-x, -y)
Step-by-step explanation:
Let us revise the rotation about the origin
- If point (x, y) rotated about the origin by angle 90° counterclockwise (or 270° clockwise), then its image is (-y, x)
. The rule is (x, y) → (-y, x)
- If point (x, y) rotated about the origin by angle 180° counterclockwise ( or 180° clockwise), then its image is (-x, -y)
. The rule is (x, y) → (-x, -y)
- If point (x, y) rotated about the origin by angle 270° counterclockwise (90° clockwise), then its image is (y, -x)
. The rule is (x, y) → (y, -x)
Let us solve the question
∵ The vertices of triangle FGH are (-6, -8), (-2, -3), (-4, -2)
∵ The figure is rotated 180° using the origin as the center of rotation
→ By using the 2nd rule above
∴ The vertices of its image are (6, 8), (2, 3), (4, 2)
∴ The rule is (x, y) → (-x, -y)
The coordinates of the vertices of the preimage compare to the coordinates of the vertices of the image do (x, y) right-arrow (negative x, negative y) ⇒ (x, y) → (-x, -y)
