Question

On a coordinate plane, a circle has a center at (negative 2, 0). Point (negative 2, 4) lies on the circle.
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot

Does the point (1, StartRoot 7 EndRoot) lie on the circle shown?
Explain.

Yes, the distance from (–2, 4) to (1, ) is 4 units.
Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.
No, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is not 4 units.
No, the distance from (–2, 4) to (1, StartRoot 7 EndRoot) is not 4 units.

Answer 1

Yes. The radius is distance from center (–2,0) to (–2,4) = 4. Using the distance formula from the center to (1, √7):

distance = sqrt[(1 - (−2))^2 + (√7 - 0)^2] = sqrt[3^2 + (√7)^2] = sqrt[9 + 7] = sqrt[16] = 4.

So the correct choice is: "Yes, the distance from (–2, 0) to (1, √7) is 4 units."