## SAT SUBJECT TEST MATH LEVEL 1

## SOLID AND COORDINATE GEOMETRY

**CHAPTER 13**

**Coordinate 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 P**

_{1}**(**

*x*

_{1}**,**

*y*

_{1}**) and**

*P*

_{2}**(**

*x*

_{2}**,**

*y*

_{2}**) 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,