Question

analyzing a students work
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 $(2, -2)$.
$\sqrt{(-1-2)^2 + (2-(-2))^2}$
$\sqrt{(-3)^2 + (0)^2} = 3$
the point $(2, -2)$ doesnt lie on the circle because the
calculated distance should be the same as the radius.
is amits 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.

Explanation:

Step1: Verify radius calculation

Radius $r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5$ units.

Step2: Check distance formula setup

Distance from $(-1,2)$ to $(2,-2)$:
$\sqrt{(-1 - 2)^2 + (2 - (-2))^2}$

Step3: Correct distance calculation

$\sqrt{(-3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$

Step4: Compare to radius

The calculated distance equals the radius, so Amit's calculation was wrong.

Answer:

No, he did not calculate the distance correctly.