Question

On a coordinate plane, a circle has a center at (0, 0). Point (0, negative 10) lies on the circle.

A circle centered at the origin contains the point
(0, –9). Does (8, StartRoot 17 EndRoot) also lie on the circle? Explain.
No, the distance from the center to the point
(8, StartRoot 17 EndRoot) is not the same as the radius.
No, the radius of 10 units is different from the distance from the center to the point
(8, StartRoot 17 EndRoot).
Yes, the distance from the origin to the point
(8, StartRoot 17 EndRoot) is 9 units.
Yes, the distance from the point (0, –9) to the point (8, StartRoot 17 EndRoot) is 9 units.

Answer 1

The distance between point $(8, \sqrt{17})$ and the center (0,0) is of 9 units, which is less than the radius, hence the correct option is:

Yes, the distance from the origin to the point $(8, \sqrt{17})$ is of 9 units.

What is the distance between two points?

Suppose that we have two points, $(x_1,y_1)$ and $(x_2,y_2)$. The distance between them is given by:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

In this problem, we have a circle with center at (0,0) and radius 10. Hence, every point that is less than 10 units of distance from point (0,0) will be on the circle.

The distance of $(8, \sqrt{17})$ is:

$D = \sqrt{(8 - 0)^2+(\sqrt{17} - 0)^2}$

$D = \sqrt{81}$

D = 9 units.

9 < 10, hence the correct option is:

Yes, the distance from the origin to the point $(8, \sqrt{17})$ is of 9 units.

More can be learned about the distance between two points at https://brainly.com/question/18345417

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