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: $(-5,-9)\to(-9,-(-5))$.

Step3: Simplify the result

$-(-5)=5$, so the new point $Q'$ is $(-9,5)$. But there is a mistake above. A rotation of $-270^{\circ}$ about the origin is equivalent to a $90^{\circ}$ counter - clockwise rotation. The rule for a $90^{\circ}$ counter - clockwise rotation of a point $(x,y)$ about the origin is $(x,y)\to(-y,x)$.
For the point $Q(-5,-9)$ with $x = - 5$ and $y=-9$, substituting into the rule gives $(-(-9),-5)=(9,-5)$.

Answer:

$Q'(9, - 5)$