Question

The point (1, 4) lies on a circle that is centered at (1, 1). Which statements are correct? Check all that apply.

The circle’s radius is 2 units.
The circle’s radius is 3 units.
The circle’s radius is 9 units.
The point (–2, 1) lies on the circle.
The point (3, 3) lies on the circle.

Answer 1

True: The circle’s radius is 3 units.
True: The point (–2, 1) lies on the circle.

Work: radius = distance from (1,1) to (1,4) = sqrt((1-1)^2+(4-1)^2)=sqrt(9)=3.
(-2,1) is distance sqrt((-2-1)^2+(1-1)^2)=sqrt(9)=3 so it’s on the circle.
(3,3) is distance sqrt((3-1)^2+(3-1)^2)=sqrt(8) ≠ 3, so it is not.
(The radius squared is 9, not the radius itself.)