1-3 Distance and Midpoints

You graphed points on the coordinate plane.

• Find the distance between two points.

• Find the midpoint of a segment.

The distance between two points is the length of the segment with those points as its endpoints.Distance is ALWAYS positive in math.

p. 25

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.

You will need a scientific calculator to do this problem

1. Put x’s and y’s in the formula2. Subtract x’s and square3. Subtract y’s and square4. Add numbers under the radical5. Take square root if answer is in decimal form.

Distance Formula

p. 26

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)

A. 4

B.

C.

D.

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

1-3 Assignment Day 1

p. 31, 13-31 oddNo work, No credit!

1-3 Distance and Midpoints Day 2

You graphed points on the coordinate plane. • Find the distance between two points.

• Find the midpoint of a segment.

Midpoint Definition

The midpoint of a segment is the point halfway between the end points of the segment.

A BM

M is the midpoint of

(reads line segment AM is congruent to line segment MB

1. Add the x’s and divide by 22. Add the y’s and divide by 2

p. 27

Midpoint Formula

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

Simplify.

Answer: The midpoint of the couch back is 6.25 feet from the wall.

A. 330 ft

B. 660 ft

C. 990 ft

D. 1320 ft

DRAG RACING The length of a drag racing strip is

mile long. How many feet from the finish line is

the midpoint of the racing strip?

1 mile = 5280 feet

Coordinate Plane Midpoint Formula

Same formula, but…1. Use it for the x coordinates.2. Use it for the y coordinates.

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)

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

Midpoint Formula

Midpoint Formula

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).

= 8 = -3

hint:

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.

Use Algebra to Find Measures

Plan Because Q is the midpoint, you know

that

Use this equation and the algebraic measures to find a value for x.

Solve

Subtract 1 from each side.

Original measure

Segment Bisector

A segment bisector is any segment, line, or line that intersects a segment at its midpoint.

What does the word bisect mean?

Bi means: two

Sector means: An area or portion, subdivision

Bisect – divide into 2 equal parts

Construction: Bisect a Segment

1. Draw a segment.2. Place the compass on one end and open the compass

bigger than half of the segment.3. Draw arcs above and below the segment.4. Without moving the compass sixe, move the point to the

other end of the segment.5. Draw arcs about and below the segment.6. Use a straightedge to connect the x’s you made above and

below the segment.7. Where this new segment crosses the 1st one is the

midpoint.See page 30 for pictures.

Assignment 1-3

p. 31, 28-30 even, 33-41 odd, 47,49No work, No credit