draw the following segment after a 90° counterclockwise rotation about the origin.

Explanation:

Step1: Recall rotation rule

For a 90 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-y,x)$.

Step2: Identify endpoints

Let's assume the endpoints of the given line - segment are $(x_1,y_1)$ and $(x_2,y_2)$. Apply the rotation rule to each endpoint: $(x_1,y_1)\to(-y_1,x_1)$ and $(x_2,y_2)\to(-y_2,x_2)$.

Step3: Plot new endpoints

Plot the new endpoints $(-y_1,x_1)$ and $(-y_2,x_2)$ on the coordinate plane.

Step4: Draw new segment

Connect the new endpoints with a straight line to get the rotated segment.

Since the original endpoints are not given, the general steps for performing the rotation are as above. If you had the actual endpoints (say the endpoints of the given segment are $(x_1,y_1)$ and $(x_2,y_2)$), you would substitute the values into the rule $(x,y)\to(-y,x)$ to get the new endpoints and then draw the segment.

Answer:

Follow the steps above to draw the rotated segment. First, find the new endpoints using the rotation rule $(x,y)\to(-y,x)$ and then connect them.