Question

the point q(-5, -9) is rotated -270° about the origin. select the location of q. (1 point)
q(9, -5)
q(5, 9)
q(9, 5)
q(-5, 9)

Explanation:

Step1: Recall rotation rule

A rotation of $- 270^{\circ}$ about the origin is equivalent to a rotation of $90^{\circ}$ clock - wise. The rule for a $90^{\circ}$ clock - wise rotation of a point $(x,y)$ about the origin is $(x,y)\to(y, - x)$.

Step2: Apply the rule

Given the point $Q(-5,-9)$, where $x=-5$ and $y = - 9$. Substitute into the rule: $(-5,-9)\to(-9,5)$. But a $-270^{\circ}$ rotation is the same as a $90^{\circ}$ counter - clockwise rotation. The rule for a $90^{\circ}$ counter - clockwise rotation of a point $(x,y)$ about the origin is $(x,y)\to(-y,x)$.
Substitute $x=-5$ and $y=-9$ into the $90^{\circ}$ counter - clockwise rotation rule: $(-5,-9)\to(9,-5)$.

Answer:

A. $Q'(9,-5)$