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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.

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Answer:

Yes, the distance from the origin to the point

(8 root 17) is 9 units.

Step-by-step explanation:

got it right

Using the distance between the two points, it is found that the correct option regarding whether the point [tex](8, \sqrt{17})[/tex] lies on the circle is:

Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is 9 units.

What is the distance between two points?

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

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

In this point, a circle centered at the origin contains the point (0, –9), hence it's radius if of 9. It means that the distance between the origin and a point on the circle can be of at most 9.

The distance between the origin (0,0) and the point [tex](8, \sqrt{17})[/tex] is given by:

[tex]D = \sqrt{(8 - 0)^2+(\sqrt{17}-0)^2} = \sqrt{81} = 9[/tex]

Hence, the correct option is:

Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is 9 units.

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

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