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

Radius = distance from (0,0) to (3,0) = sqrt((3-0)^2+(0-0)^2) = 3.

Distance from (0,0) to (2,√6) = sqrt(2^2+(√6)^2) = sqrt(4+6) = √10 ≈ 3.162, which is not 3.

So: No — the distance from (0,0) to (2,√6) is not 3 units.