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: (2, -3) point in final figure: (2, 3)

Explanation:

Step1: Recall rotation rule

The rule for rotating a point $(x,y)$ 180° counter - clockwise about the origin is $(x,y)\to(-x,-y)$.

Step2: Apply rule to given point

Given the original point $(2, - 3)$. Using the rule, $x = 2$ and $y=-3$, so $-x=-2$ and $-y = 3$. The new point should be $(-2,3)$ (it seems there is an error in the provided final - point coordinates in the original problem statement).

Answer:

Point in original figure: $(2,-3)$
Point in final figure: $(-2,3)$