Question

the figure below has a point marked with a large dot. first, rotate the figure 270° 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: Recall rotation rule

The rule for rotating a point $(x,y)$ 270° counter - clockwise about the origin is $(x,y)\to(y, - x)$.

Step2: Assume original point coordinates

Let the coordinates of the marked point in the original figure be $(x,y)$.

Step3: Find final point coordinates

Using the rotation rule, the coordinates of the point in the final figure after a 270° counter - clockwise rotation about the origin will be $(y,-x)$.

Answer:

Since no specific coordinates of the marked point in the original figure are given in the question, we can only state the general rule.
Point in original figure: $(x,y)$
Point in final figure: $(y, - x)$