Question

the figure below has a point marked with a large dot. first, rotate the figure 270° clockwise 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

From the graph, the coordinates of the marked - point in the original figure are $(-2,3)$.

Step2: Apply rotation rule

The rule for a $270^{\circ}$ clock - wise rotation about the origin is $(x,y)\to(y, - x)$.
For the point $(-2,3)$, substituting $x=-2$ and $y = 3$ into the rule:
The new $x$ - coordinate is $y = 3$ and the new $y$ - coordinate is $-x=-(-2)=2$.

Answer:

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