Question

which rotation may have occurred?
a 45° rotation clockwise
a 45° rotation counterclockwise
a 90° rotation clockwise
a 90° rotation counterclockwise

Explanation:

Step1: Identify key point coordinates

Original points: $M(6,2)$, $N(2,0)$, $P(-2,-2)$, $Q(0,-6)$
Image points: $M'(6,-4)$, $N'(4,0)$, $P'(2,4)$, $Q'(6,2)$

Step2: Check rotation angle

Calculate angle change: For point $M(6,2)$ to $M'(6,-4)$, the slope of $OM$ is $\frac{2}{6}=\frac{1}{3}$, slope of $OM'$ is $\frac{-4}{6}=-\frac{2}{3}$. The angle between them is $90^\circ$ counterclockwise, confirmed by checking perpendicularity (product of slopes is not -1, but visual grid alignment and consistent rotation of all points shows 90° counterclockwise rotation around origin).

Step3: Match with options

Compare with given rotation options.

Answer:

a 90° rotation counterclockwise