1.3: Distance and Midpoints

Objective: I will be able to…-Calculate the distance between 2

points-Calculate the midpoint of 2 points

You graphed points on the coordinate plane.

• Find the distance between two points.

• Find the midpoint of a segment.

Distance: the length of the segment between 2 points

Irrational number: a number that cannot be expressed as a terminating or repeating decimal

Midpoint: the point that is halfway between the endpoints of a line segment

Segment Bisector: any segment, line, or plane that intersects a segment at its midpoint

NEW VOCAB!

Real world examples

-Get into groups

-Complete front and back of worksheet together

-I want to see some serious explanations! No one word answers or “I don’t know”!

Let’s discover the distance formula!First, we’ll plot two points:

(0,0) and (3,4)

We want to calculate the shortest distance between these two points.

We will create a right triangle.

How do we find the lengths of our legs?

What side is the “distance” on?

Find Distance on a Coordinate Plane

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

A. 4

B.

C.

D.

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

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? (Remember: 1 mile = 5,280 feet)

Let’s discover the midpoint formula!Graph 2 points J (1,2) and E (-3,5)

We will draw a line segment between them

Thinking back to how we find a midpoint on a number line, how do you think we find a midpoint on a coordinate plane?

A. (–10, –6)

B. (–5, –3)

C. (6, 12)

D. (–6, –12)

Find the Coordinates of an Endpoint

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).

A. 1

B. 10

C. 5

D. 3

Segment Bisector: any segment, line, or plane that intersects a segment at its midpoint

A

B

P

Q

A

B C

E

D

Homework Assignment

pg. 31 #22-24, 31-32, 47-49, 68