Answer:
The point that lies on the circle is point A since the distance from point A to the center is equal to the radius of the circle.
Explanation:
In order for the points to lie on the circle the distance from the center of the circle to the point must be equal to the radius of the circle (5 units). The distance between points can be computed by the formula below:
distance = sqrt[(x1 - x2)² + (y1 - y2)²]
So for point A:
distance = sqrt[(-3 - (-7))² + (-3 - (-6))²]
distance = sqrt[(4)² + (3)²] = sqrt[16 + 9] = sqrt(25) = 5
Since the distance is equal to the radius the point lies on the circle.
For point B we don't need to calculate, since it's the same point as the center, therefore it can't be on the circle.
For point C:
distance = sqrt[(-3 - (6))² + (-3 - (7))²]
distance = sqrt[(-9)² + (-10)²] = sqrt[81 + 100] = sqrt(181) = 13.45
Not on the circle.
For point D:
distance = sqrt[(-3 - (9))² + (-3 - (9))²]
distance = sqrt[(-12)² + (-12)²] = sqrt[144 + 144] = sqrt(288) = 16.97
Not on the circle.