Question

Which point is on the circle centered at the origin with a radius of 5 units?

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

(2, StartRoot 21 EndRoot)
(2, StartRoot 23 EndRoot)
(2, 1)
(2, 3)

Answer 1

Use the distance from the origin: x^2 + y^2 must equal 25.

- (2, √21): 2^2 + (√21)^2 = 4 + 21 = 25 → on the circle.
- (2, √23): 4 + 23 = 27 → no.
- (2, 1): 4 + 1 = 5 → no.
- (2, 3): 4 + 9 = 13 → no.

So (2, √21) is on the circle.