Question

writing a rule for a rotation
what rule describes the rotation about the origin?
(x, y)→
how many degrees was the figure rotated about the
(y, -x)
(-y, x)
(-x, -y)
(x, y)

Explanation:

Step1: Recall rotation rules

In a 90 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-y,x)$. In a 90 - degree clockwise rotation about the origin, the rule is $(x,y)\to(y, - x)$. In a 180 - degree rotation about the origin, the rule is $(x,y)\to(-x,-y)$. In a 360 - degree rotation about the origin, the rule is $(x,y)\to(x,y)$.

Step2: Analyze the figure

By observing the pre - image $\triangle ABC$ and the image $\triangle A'B'C'$, we can see that it is a 90 - degree counter - clockwise rotation. The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.

Answer:

$(x,y)\to(-y,x)$