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.

Question

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Respuesta :

Rasneet Rasneet · Answer 1 · 2021-05-07T03:04:02+02:00

Answer:

3rd

C

Explanation:

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

Answer Link

MrRoyal MrRoyal · Answer 2 · 2022-05-16T13:14:12+02:00

The point (2,-2) is on the circle, and Amit's claim is wrong

The given parameters are:

Center = (-1,2)

Diameter = 10 units

Point = (2,-2)

Start by calculating the radius, r

r = diameter/2

r = 10/2

r = 5

Next, calculate the distance from the point to the center using:

[tex]r = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

This gives

[tex]r = \sqrt{(2 + 1)^2 + (-2-2)^2}[/tex]

Evaluate

r = 5

The distance from the center to the point equals the radius of the circle

Hence, the point is on the circle, and Amit's claim is wrong

Read more about circle equations at:

https://brainly.com/question/1559324

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