Question

On a coordinate plane, a circle has a center at (0, 0). Point (3, 0) lies on the circle.

Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot

Does the point (2, StartRoot 6 EndRoot) lie on the circle shown? Explain.

Yes, the distance from (3, 0) to (0, 0) is 3 units.
Yes, the distance from (0, 0) to (2, StartRoot 6 EndRoot) is 3 units.
No, the distance from (3, 0) to (2, StartRoot 6 EndRoot) is not 3 units.
No, the distance from (0, 0) to (2, StartRoot 6 EndRoot) is not 3 units

Answer 1

No. The radius is the distance from (0,0) to (3,0) = 3, so r^2 = 9. For (2, √6), x^2 + y^2 = 2^2 + (√6)^2 = 4 + 6 = 10 ≠ 9, so its distance from (0,0) is √10 (about 3.162), not 3. Thus (2, √6) is not on the circle.