Question

A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?

Answer 1

Use the distance formula to find the length of a line from the origin (0,0) and (5,-12). As the center of the circle is at the origin, and (5,-12) is a point on the circle, the line connecting those points is a radius.

Distance formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is
\[d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\]

If you draw a sketch, you should be able to convince yourself that this is just the Pythagorean theorem in disguise.

Answer 2

Thanks!