Question

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

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 brainly.com/question/18345417

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