The figure shows line segment PQ and a

Adam Lyons, Magoosh Tutor

Hi Casey,
Happy to help :)
Yes, we could draw a point farther from Q. But in order to be farther from Q, this point must be closer to P. And remember that we aren't looking for distances from Q, we're looking for distances from anywhere on the segment PQ. So the distance from Q (or P) to (6, 2) is the largest possible distance from a point on the circle to a point on the segment PQ. Anything farther from Q than that will be closer to P, and thus closer to a point on the segment PQ.
Hope that helps!

Dec 26, 2019 • Reply

Adam Lyons, Magoosh Tutor

You got it: the questions specifies the distance between a point on the line segment and a point on the circumference of the circle. The inside of the circle, within it, does not count. "On" the circle means on the circumference of the circle. "In" the circle would mean inside or within it. But we need points on the circumference alone. So the distance should be between any point on the line segment and any point on the circumference of the circle.

Jul 21, 2019 • Reply

Lucas Fink, Magoosh Tutor

Good question, Angela! The far point of the circle is (6,2), it's true. However, that's only 5 away from the line segment QP at minimum, because QP is at the value of 1 on the x-axis. Since 6-1=5, the distance from the middle of QP to the far end of the circle is 5. I hope that helps :-)

Jun 7, 2013 • Reply

Cristina Velasquez

Hello, Could you please explain how you knew that one of the points was 3.0 of distance away ? Thank you!

Apr 22, 2014 • Reply

Lucas Fink, Magoosh Tutor

Christina— the point on the left side of the circle is 1 away from the center of the circle because the circle has a radius of 1. So that point would be (4,2). that is the closest part of the circle to the line, because it's the point on the circle that is leftmost.

Meanwhile, the point on the line that is closest to the circle is in the center of the line. If you move up or down the line, you can see that it moves away from the circle. That point in the center of the line is (1,2).

We know there is a distance of 3 from those two points— (4,2) (1,2)—by simple subtraction. The y coordinates are the same, so we only care about the 4 and the 1. The distance from 4 to 1 is 3 because 4-1 = 3.

Apr 26, 2014 • Reply