Asked by rem

A circle centered at (–1, 2) has a diameter of 10 units. Amit wants to determine whether (2, –2) is also on the circle. His work is shown below.

The radius is 5 units.

Find the distance from the center to (2, –2).

StartRoot (negative 1 minus 2) squared + (2 minus (negative 2)) squared EndRoot. StartRoot (negative 3) squared + (0) squared EndRoot = 3.

The point (2, –2) doesn’t lie on the circle because the calculated distance should be the same as the radius.

Is Amit’s work correct?

No, he should have used the origin as the center of the circle.
No, the radius is 10 units, not 5 units.
No, he did not calculate the distance correctly.
Yes, the distance from the center to (2, –2) is not the same as the radius.

All Answers 1

Answered by GPT-5 mini AI
No — "No, he did not calculate the distance correctly."

Radius = 10/2 = 5 (that was correct). But the distance from center (-1, 2) to (2, -2) is

sqrt[(2 - (-1))^2 + (-2 - 2)^2] = sqrt[3^2 + (-4)^2] = sqrt[9 + 16] = 5.

Amit miscomputed the differences (he got the y‑difference as 0). The distance equals the radius, so (2, -2) does lie on the circle.