﻿ THE MIDPOINT OF A SEGMENT - Coordinate Geometry - SOLID AND COORDINATE GEOMETRY - SAT SUBJECT TEST MATH LEVEL 1 ﻿

## CHAPTER 13Coordinate Geometry

### THE MIDPOINT OF A SEGMENT

Recall that the midpoint, M, of line segment  is the point on  such that PM = MQ. In coordinate geometry, the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.

Key Fact L4

If P1(x1y1) and P2(x2y2) are any two points, then the midpoint, M, of segment  is the point whose coordinates are .

EXAMPLE 3: If C(3, –4) and D(7,2) are the endpoints of diameter CD of circle O, what are the coordinates of O?

First, sketch the circle (see diagram). Since the center of a circle is the midpoint of any diameter, we can use the midpoint formula to find the coordinates of O.

EXAMPLE 4: To find the area of circle O in Example 3, we have to use the formula A = πr 2, which means we have to determine r. To do this, we can either find the length of diameter  and divide it by 2 or find the length of radius .

Then, depending on which expression you found,

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