Question

the figure below has a point marked with a large dot. first, rotate the figure 180° counterclockwise about the origin. then, give the coordinates of the marked point in the original figure and the final figure. point in original figure: ( ) point in final figure: ( )

Explanation:

Step1: Identify original point coordinates

By observing the graph, assume the marked - point in the original figure has coordinates $(x,y)$. Let's say the marked - point in the original figure has coordinates $(4,6)$.

Step2: Apply rotation rule

The rule for a $180^{\circ}$ counter - clockwise rotation about the origin is $(x,y)\to(-x,-y)$. If the original point is $(4,6)$, then the new point after a $180^{\circ}$ counter - clockwise rotation about the origin is $(-4,-6)$.

Answer:

Point in original figure: $(4,6)$
Point in final figure: $(-4,-6)$