Distance and Midpoint Formulas

Distance between two points

1. Using the formula, find the distance between (-2, 5) and (3, -1)

Midpoint Formula- finds the point that is equidistance from two endpoints.

M =

2. Find the midpoint of the line jointing (6, -2) and (2, -9)

Finding perpendicular bisectors of a segment

Step 1- find the midpoint of the segment

Step 2- find the slope of the segment

Step 3- use point slope to find the equation of the line perpendicular to the line segment at the midpoint. Use the negative reciprocal for the slope and the midpoint of the segment.

3. Write the equation of the perpendicular bisector of the line segment joining (-2,1) and (1,4)

In Geometry you learned that the perpendicular bisector of a chord of a circle passes through the center of the circle. Using this theorem you can find the center of a circle given three points on the circle.

Read the example, follow the steps to find the center of the circle.

While on an archeological dig, you discover a piece of a broken dish. To estimate the original diameter of the dish, you lay the piece on a coordinate plane and mark three points on the circular edge, as shown. Use these points to find the diameter of the dish.(each unit represents one inch.)

Step 1: Find the perpendicular bisectors of AO and BO

Step 2: Both bisectors pass through the center of the circle. Therefore, the center of the circle is the solution of the system formed by these two equations. Solve the system to find the center. Use elimination, substitution or graphing. Find the center point.

Step 3: The radius of the circle is the distance from the center to a point on the circle. Use the center point you found in step 2 and the distance formula to find the radius. Multiply the radius by 2 and you have the diameter.