Question

what is the image of the point (3, - 4) after a rotation of 180° counterclockwise about the origin?

Explanation:

Step1: Recall rotation rule

When a point $(x,y)$ is rotated 180° counter - clockwise about the origin, the new coordinates $(x',y')$ are given by $x'=-x$ and $y'=-y$.

Step2: Apply rule to given point

For the point $(3, - 4)$, where $x = 3$ and $y=-4$, we have $x'=-3$ and $y'=-(-4)=4$.

Answer:

$(-3,4)$