Think how a single point can be rotated 90^(∘) clockwise about the origin.
C
Practice makes perfect
We are given △ ABC, where A(5,1), B(3,7), and C(2,2). This triangle is rotated 90^(∘) clockwise about the origin. We want to find the coordinates of point B after the rotation. To do so, let's perform the rotation ourselves. FIrst, let's draw the original triangle.
Now, let's think about how a single point can be rotated in this way. To rotate point A 90^(∘) clockwise about the origin we should draw a line segment that connects A with the origin. Then we should draw a line segment of the same length and perpendicular to the previous segment. Furthermore, the directed angle between the two segments should be -90^(∘).
To rotate the entire triangle, we should rotate each of its vertices separately. After doing so, we can connect the rotated vertices and the resulting polygon is the rotated triangle.
Looking at the result, we see that point B after the rotation is a point that has a positive x-coordinate and a negative y-coordinate. Among the given pairs of coordinates (7,-3) is the only pair with these properties. Looking again at the diagram, this point fits the rotated point exactly. Therefore, answer C is correct.
