the line segment AB is rotated through 90° clockwise about the point C. the coordinates of A', the image of A, are​

B

Step-by-step explanation:

We dont know rules about rotating a point. We only know rules about rotating about the orgin.

We can translate this line segment so point c is on the orgin because

Point C is at (1,3) so let move this all points 1 to the left and 3 down. Why All Points?

A translation is parallel from it original image to its second or new image so this means Point B and Point A will both move as well. Let just focus on Point A. The new coordinates are:

Let apply the 90 degree clockwise rule. Point C doesnt move since it is at the orgin and it at the center of rotation.

(x,y) goes to (y,-x).

So Point A prime is now at

(0,-1).

Now let translate the figure back to Point C (1,3). by going 1 to the right and 3 up so our new point of Point A prime is at

(1,2).