Question

what transformation is represented by the rule (x, y) into (-x, -y)?
180 degree rotation about the origin
reflection across the x axis
reflection across the y axis
rotation 90 counter clockwise about the origin
rotation 90 clockwise about the origin

Explanation:

Step1: Recall transformation rules

For a 180 - degree rotation about the origin, the rule is $(x,y)\to(-x, -y)$. 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 90 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-y,x)$. For a 90 - degree clockwise rotation about the origin, the rule is $(x,y)\to(y, -x)$.

Answer:

180 degree rotation about the origin