Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Warm Up

1. Graph A (–2, 3) and B (1, 0).

2. Find CD. 8

3. Find the coordinate of the midpoint of CD. –2

4. Simplify.

4

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Develop and apply the formula for midpoint.

Use the Distance Formula and the Pythagorean Theorem to find the distance between two points.

Objectives

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

You can find the midpoint of a segment by using the coordinates of its endpoints.

To find the midpoint:Calculate the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

To make it easier to picture the problem, plot the segment’s endpoints on a coordinate plane.

Helpful Hint

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Example 1: Finding the Coordinates of a Midpoint

Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Check It Out! Example 1

Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Example 2: Finding the Coordinates of an Endpoint

M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y.

Step 1 Let the coordinates of Y equal (x, y).

Step 2 Use the Midpoint Formula:

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Example 2 Continued

Step 3 Find the x-coordinate. Find the y coordinate

Set the coordinates equal.

Multiply both sides by 2.

12 = 2 + x Simplify.

– 2 –2

10 = x

Subtract.

Simplify.

2 = 7 + y– 7 –7

–5 = y

The coordinates of Y are (10, –5).

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Check It Out! Example 2

S is the midpoint of RT. R has coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T.

Step 1 Let the coordinates of T equal (x, y).

Step 2 Use the Midpoint Formula:

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Check It Out! Example 2 Continued

Step 3 Find the x-coordinate. Find the y-coordinate

Set the coordinates equal.

Multiply both sides by 2.

–2 = –6 + x Simplify.

+ 6 +6

4 = x

Add.

Simplify.

2 = –1 + y+ 1 + 1

3 = y

The coordinates of T are (4, 3).

Holt McDougal Geometry

1-6 Midpoint and Distance in the Coordinate Plane

Lesson Quiz: Part I

(17, 13)

(3, 3)1. Find the coordinates of the midpoint of MN with

endpoints M(-2, 6) and N(8, 0).

2. K is the midpoint of HL. H has coordinates (1, –7), and K has coordinates (9, 3). Find the coordinates of L.