Suppose triangle abc has vertices at a(1, 0), b(10, 0), and c(2, 6). after a 60° counterclockwise rotation about the origin, vertex b' has coordinates (5,

Check the picture attached.

Let OB be the radius of circle with center O.

Let B' be the image of B after the described rotation

OB and OB' are sides of the equilateral triangle OBB'.

The x coordinate of B' is the midpoint of OB, that is 5.

In the right triangle B', point (5, 0) and B:

Distance point (5, 0) to B is 5
|B'B|=|OB|=10

so by the pythagorean theorem:

units

 

Cwill be your correct answer