Question

what transformation is represented by the rule (x, y) → (-x, - y)? rotation of 90° counterclockwise about the origin reflection across the x - axis reflection across the y - axis rotation of 180° about the origin

Explanation:

1. Recall transformation rules:

• For a 90 - degree counter - clockwise rotation about the origin, the rule is \((x,y)\to(-y,x)\).
• For a reflection across the x - axis, the rule is \((x,y)\to(x, - y)\).
• For a reflection across the y - axis, the rule is \((x,y)\to(-x,y)\).
• For a 180 - degree rotation about the origin, we change the sign of both x and y coordinates. The rule \((x,y)\to(-x,-y)\) represents a 180 - degree rotation about the origin.

Answer:

D. rotation of 180° about the origin