Question

A circle is drawn on a coordinate grid. Which statement is true?

a) Every line with a positive slope must either intersect the circle or be tangent to it.
b) The distance between two points on the circle can never be greater than the length of the circle’s radius.
c) Any line must meet the circle at either 0, 1, or 2 points.
d) If two points are inside the circle, the distance between them can be greater than the length of the circle’s diameter.

Answer 1

The statement that is true for a circle drawn on a coordinate grid is that any line must meet the circle at either 0, 1, or 2 points.

Step-by-step explanation:

The correct statement is option c) Any line must meet the circle at either 0, 1, or 2 points.

This is because a line can be completely outside the circle and not intersect it at all (0 points), it can intersect the circle at a single point (1 point), or it can intersect the circle at two points (2 points).

For example, if we have a line with negative slope, it will not intersect the circle at all. If we have a line with positive slope, it can intersect the circle at two points if it passes through it, or at one point if it is tangent to the circle.