Question

the point p (4,2) is rotate to become p(-2,4). describe the rotation by degree and direction. (1 point) 90° rotation -90° rotation -270° rotation 180° rotation

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation of a point $(x,y)$ about the origin, the new point $(x',y')$ is given by $(-y,x)$. For a 90 - degree clockwise rotation (or - 90 degree counter - clockwise rotation), the new point of $(x,y)$ is $(y, - x)$. For a 180 - degree rotation, the new point of $(x,y)$ is $(-x,-y)$. For a 270 - degree counter - clockwise rotation (or - 90 degree clockwise rotation), the new point of $(x,y)$ is $(y,-x)$.
The original point is $P(4,2)$ and the new point is $P'(-2,4)$.
If we apply the 90 - degree counter - clockwise rotation rule: when $x = 4$ and $y = 2$, $x'=-y=-2$ and $y' = x = 4$.

Answer:

90° rotation (counter - clockwise)

(Note: In the multiple - choice context, the correct option is the one with 90° rotation. Since the rule for 90° counter - clockwise rotation matches the transformation from $(4,2)$ to $(-2,4)$, and usually when we just say 90° rotation without further specification, we mean counter - clockwise in a coordinate - geometry context).