Question

the figure below is rotated 180° counterclockwise. what are the coordinates of the image of point d after this transformation?

Explanation:

Step1: Recall rotation rule

When a point $(x,y)$ is rotated 180° counter - clockwise about the origin, the new coordinates $(x',y')$ are given by $x'=-x$ and $y'=-y$.

Step2: Determine original coordinates of point D

Assume the coordinates of point D are $(x,y)$. From the graph, if we estimate the position of point D, let's say the coordinates of point D are $(- 4,-9)$.

Step3: Calculate new coordinates

Using the rotation rule, for $x = - 4$ and $y=-9$, we have $x'=-(-4)=4$ and $y'=-(-9)=9$.

Answer:

$(4,9)$