Question

1. circle p is centered at the origin. which of the following statements can be used to construct an algebraic proof the point a lies on circle p?

based on visual inspection, point a lies on circle p. therefore, point a lies on circle p.

the distance from the origin to point a is greater than the radius of circle p. therefore, point a lies on circle p.

the distance from the origin to point a is equal to the radius of circle p. therefore, point a lies on circle p.

the distance from the origin to point a is less than the radius of circle p. therefore, point a lies on circle p.

Explanation:

To determine if a point lies on a circle, the key concept is that the distance from the center (origin here) to the point must equal the radius.

• The first option uses visual inspection, not an algebraic proof.
• The second option says distance > radius, which means the point is outside the circle, not on it.
• The third option states distance = radius, which is the correct condition for a point to lie on a circle.
• The fourth option says distance < radius, meaning the point is inside the circle, not on it.

Answer:

C. The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P.