Question

On a coordinate plane, a circle has a center at (0, 0). Point (0, negative 10) lies on the circle.
A circle centered at the origin contains the point
(0, –9). Does (8, StartRoot 17 EndRoot) also lie on the circle? Explain.

No, the distance from the center to the point
(8, StartRoot 17 EndRoot) is not the same as the radius.
No, the radius of 10 units is different from the distance from the center to the point
(8, StartRoot 17 EndRoot).
Yes, the distance from the origin to the point
(8, StartRoot 17 EndRoot) is 9 units.
Yes, the distance from the point (0, –9) to the point (8, StartRoot 17 EndRoot) is 9 units.

Answer 1

Answer: Yes — "the distance from the origin to the point (8, √17) is 9 units."

Reason: The circle that contains (0, −9) and is centered at the origin has radius 9. Compute the distance from the origin to (8, √17):
distance = sqrt(8^2 + (√17)^2) = sqrt(64 + 17) = sqrt(81) = 9.
Since this equals the radius, (8, √17) lies on the circle.

(Other choices are incorrect: the circle with (0,−10) would have radius 10, and the distance between (0,−9) and (8, √17) is not 9.)