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: Identify original - point coordinates

The marked point in the original figure is at $(4,2)$ by observing its position on the coordinate - grid (4 units to the right of the y - axis and 2 units above the x - axis).

Step2: Apply rotation rule

The rule for rotating a point $(x,y)$ counterclockwise about the origin by $270^{\circ}$ is $(x,y)\to(y, - x)$. For the point $(4,2)$, substituting $x = 4$ and $y = 2$ into the rule, we get $(2,-4)$.

Answer:

Point in original figure: $(4,2)$
Point in final figure: $(2,-4)$