Chapter 1.3

Distance and Measurement

Distance (between two points)- the length of the segment with those points as its endpoints.

Definition

Concept

Find Distance on a Number Line

Use the number line to find QR.

The coordinates of Q and R are –6 and –3.

QR = | –6 – (–3) | Distance Formula

= | –3 | or 3 Simplify.

Answer: 3

A. 2

B. 8

C. –2

D. –8

Use the number line to find AX.

Concept

Find Distance on a Coordinate Plane

Find the distance between E(–4, 1) and F(3, –1).

(x1, y1) = (–4, 1) and (x2, y2) = (3, –1)

Find Distance on a Coordinate Plane

Check Graph the ordered pairs and check by using the Pythagorean Theorem.

Find Distance on a Coordinate Plane

.

Find the distance between A(-3, 8) and

B(-5, 2)

A. 4

B.

C.

D.

Find the distance between A(–3, 4) and M(1, 2).

Concept

Example 3 Find Midpoint on a Number Line

DECORATING Marco places a couch so that its end is perpendicular and 2.5 feet away from the wall. The couch is 90” wide. How far is the midpoint of the couch back from the wall in feet?

First we must convert 90 inches to 7.5 feet. The coordinates of the endpoints of the couch are 2.5 and 10. Let M be the midpoint of the couch.

Midpoint Formula

x1 = 2.5, x2 = 10

Example 3

A. 330 ft

B. 660 ft

C. 990 ft

D. 1320 ft

The length of a drag racing strip is a quarter of a mile long. How many feet from the finish line is the midpoint of the racing strip?

Concept

Find Midpoint in Coordinate Plane

Answer: (–3, 3)

A. (–10, –6)

B. (–5, –3)

C. (6, 12)

D. (–6, –12)

Find the Coordinates of an Endpoint

Write two equations to find the coordinates of D.

Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula.

(x2, y2) = (–5, –3)

Find the Coordinates of an Endpoint

Answer: The coordinates of D are (–7, 11).

Midpoint Formula

Midpoint Formula

• Find the coordinates of the missing endpoint if Y is the midpoint of XZ:

X(-4, 2) and Y(6, -1)

A. (3.5, 1)

B. (–10, 13)

C. (15, –1)

D. (17, –11)

Find the coordinates of R if N (8, –3) is the midpointof RS and S has coordinates (–1, 5).

Segment Bisector

Any segment, line, or plane that intersects a segment at its midpoint is called a segment bisector. In the figure, M is the midpoint of line AB. Line XY is the segment bisector of line AB.

X

Y

M

Use Algebra to Find Measures

Understand You know that Q is the midpoint of PR, and the figure gives algebraic measures for QR and PR. You are asked to find the measure of PR.

• Suppose S is the midpoint of RT. RS = 3x – 4,

ST = 5x – 26, Find the measure of RT.

A. 1

B. 10

C. 5

D. 3

Pg. 30 #1-12

Try it!