1. 1.3: Distance and Midpoints
Objective: I will be able to…
-Calculate the distance between 2 points
-Calculate the midpoint of 2 points

2. You graphed points on the coordinate plane.
Find the distance between two points.
Find the midpoint of a segment.
Then/Now

3. NEW VOCAB!
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

4. 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”!

5. 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?

6. Concept

7. Find the distance between E(–4, 1) and F(3, –1).
Find Distance on a Coordinate Plane
Find the distance between E(–4, 1) and F(3, –1).
Example 2

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

9. Concept

10. DRAG RACING The length of a drag racing strip is. mile long
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)
A. 330 ft
B. 660 ft
C. 990 ft
D ft
Example 3

11. 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?

12. Concept

13. A. (–10, –6)
B. (–5, –3)
C. (6, 12)
D. (–6, –12)
Example 4

14. Find the Coordinates of an Endpoint
Example 5

15. Find the coordinates of R if N (8, –3) is the midpoint of RS and S has coordinates (–1, 5).
B. (–10, 13)
C. (15, –1)
D. (17, –11)
Example 5

16. A. 1
B. 10
C. 5
D. 3
Example 6

17. Segment Bisector: any segment, line, or plane that intersects a segment at its midpointQ A B P

18. E A B C D

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