Question

the coordinates for a point and its image are q (-3,-5) and q (5, -3). based on the mapping rules for rotations, which transformation occurred? (1 point) a 90 - degree (counterclockwise) rotation a reflection across the x - axis a 180 - degree rotation a 270 - degree (counterclockwise) rotation

Explanation:

Step1: Recall 90 - degree ccw rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.
For point $Q(-3,-5)$, applying the rule: $x=-3,y = - 5$. Then $-y=-(-5) = 5$ and $x=-3$ becomes the new $y$ - coordinate. The new point is $(5,-3)$ which is $Q'$.

Step2: Check other transformation rules

For a reflection across the $x$ - axis, the rule is $(x,y)\to(x,-y)$. For $Q(-3,-5)$, it would be $(-3,5)$.
For a 180 - degree rotation, the rule is $(x,y)\to(-x,-y)$. For $Q(-3,-5)$, it would be $(3,5)$.
For a 270 - degree counter - clockwise rotation (same as 90 - degree clockwise), the rule is $(x,y)\to(y,-x)$. For $Q(-3,-5)$, it would be $(-5,3)$.

Answer:

a 90 - degree (counterclockwise) rotation