Question

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). $sqrt{(-1 - 2)^2+(2-(-2))^2}$ $sqrt{(-3)^2+(4)^2}=5$ 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: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, the center of the circle is $(x_1,y_1)=(-1,2)$ and the point is $(x_2,y_2)=(2,-2)$.

Step2: Calculate distance

$d=\sqrt{(-1 - 2)^2+(2-(-2))^2}=\sqrt{(-3)^2+(4)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.
The radius of the circle is $r=\frac{diameter}{2}=\frac{10}{2}=5$ units. Since the calculated distance from the center $(-1,2)$ to the point $(2,-2)$ is equal to the radius, Amit made a mistake in distance - calculation. He incorrectly calculated $\sqrt{(-3)^2+(0)^2}$ instead of $\sqrt{(-3)^2+(4)^2}$.

Answer:

No, he did not calculate the distance correctly.