Question

A circle centered at the origin contains the point
(0, -9). Does (8, 17) also lie on the circle? Explain.
c
O No, the distance from the center to the point
(8, 17) is not the same as the radius.
+
O No, the radius of 10 units is different from the
distance from the center to the point
(8, V17).
-10
-8
-6
-4
-2
10
O
Yes, the distance from the origin to the point
(8. 17) is 9 units.
O
Yes, the distance from the point (0, -9) to the point
(8, 17) is 9 units.

Answer 1

Answer:

Yes, the distance from the origin to the point (8,√17) is 9 units.

Step-by-step explanation:

The equation of a circle centered at the origin with radius , r has equation:

${x}^{2} + {y}^{2} = {r}^{2}$

Since the circle passes through (0,-9), the radius is 9 units because (0,-9) is 9 units from the origin.

We substitute the radius to get:

${x}^{2} + {y}^{2} = {9}^{2}$

${x}^{2} + {y}^{2} = 81$

If (8,√17) lies on this circle, then it must satisfy this equation:

${8}^{2} + { (\sqrt{17} )}^{2} = 64 + 17 = 81$

This is True.

This means the distance from (8,√17) is 9 units from the origin.

Answer 2

Answer:

The answer is C, Yes, the distance from the origin to the point

(8, 17) is 9 units.

Step-by-step explanation: