Jessica S. answered • 01/12/22
Graduate of UCF; MS in Chemistry, MS in Forensic Science
By definition, the radius of a circle must go from the center of the circle to a point on the circle, and we are given the coordinates of both of these points. If you were to plot those two points on graph paper, then all you would need is to calculate the distance between them.
The easiest way to do this is with the distance formula, which comes from the pythagorean theorem. The formula is (x2 - x1)2 + (y2 - y1)2 = d2, where the two points you were given are (x1, y1) and (x2, y2), and d is the distance between them. Once you plug the values into this formula, you can solve for the distance between them, "d", which would be your radius.
Try drawing these two points on graph paper and connecting them with a single line segment. That segment then is the hypotenuse of a right triangle. The quantity (x2 - x1) is the length of side a; the quantity (y2 - y1) is the length of side b, and the radius of the circle is the hypotenuse of the triangle (side c). Since a2 + b2 = c2 for all right triangles, the radius is readily calculated from there; this is where the distance formula comes from. Hope this is helpful!
