Question

Which point is on the circle centered at the origin with a radius of 5 units?

Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot

A. (2, StartRoot 21 EndRoot)
B. (2, StartRoot 23 EndRoot)
C. (2, 1)
D. (2, 3)

Answer 1

Answer:

A

Step-by-step explanation:

sqrt[(2 - 0)² + (sqrt(21) - 0)²]

sqrt(4 + 21)

sqrt(25)

5

Answer 2

The only point that is in the circle of radius 5 is the option A: (2, √21).

Which point is on the circle?

We know that our circle has a radius of 5 units and it is centered at the origin, so any point that is at a distance of 5 units of the origin will be on the circle.

The distance between a point (x, y) and the origin is:

d = √(x^2 + y^2).

Of the given options, the only one that meets this condition is the one in option A. (2, √21).

If we find the distance to the origin, we get:

d = √(2^2 + √21^2) = √(4 + 21) = 5.

So that is the correct option.

If you want to learn more about circles, you can read:

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