Question

Point C(4,2) lies on a circle centered at A(1,3) if:

A. The distance between C and A is equal to the radius
B. The slope between C and A is constant
C. The sum of the coordinates of C and A is equal to the radius
D. The coordinates of C are the same as A

Answer 1

The distance between C and A is equal to the radius of the circle. option a

Step-by-step explanation:

The correct answer is A. The distance between C and A is equal to the radius.

In a circle, the radius is the distance from the center of the circle to any point on the circumference. So, if point C lies on a circle centered at point A, then the distance between C and A is equal to the radius of the circle.

To calculate the distance between any two points, we can use the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the distance between C(4,2) and A(1,3) is d = sqrt((4 - 1)^2 + (2 - 3)^2) = sqrt(9 + 1) = sqrt(10). Option a