1. Lesson 1.3 Distance and Midpoints

2. Distance Formula
Number Line -3 4 P Q

3. Distance Formulas Cont.
Coordinate Plane
The distance d between two points with coordinates and

4. Distance Examples
Number Line
Use the number line to find QR

5. Answer The coordinates of Q and R are –6 and –3.
QR = | –6 – (–3) | Distance Formula
= | –3 | or 3 Simplify.

6. Another Number Line Example
Use the number line to find AX

7. Answer The coordinates of A and X are -5 and 3
AX = |-5 – 3| Distance Formula
AX = |-8|
AX = 8

8. More Distance Examples
Coordinate Plane
Find the distance between E and F

9. Answer
The coordinates are E(-4, 1) and F(3, -1)
Label them

10. Another Example
Find the distance between A and M

11. Answer The coordinates are A(-3, 4) and M(1, 2)
Label (-3, 4) and (1, 2), and

12. Midpoint Formula Number Line
The coordinate of the midpoint of a segment with endpoints that have coordinates a and b is

13. Midpoint Cont. Coordinate Plane
The coordinates of the midpoint of a segment with endpoints that have coordinates and

14. Midpoint Examples
The coordinates on a number line Y and O are 7 and -15 respectively. Find the coordinate of the midpoint of segment YO.

15. Answer
Coordinate of the midpoint of YO is -4

16. More Examples
Find the coordinates of M, the midpoint of segment GH for G(8, -6) and H (-14, 12)

17. Answers

18. More Examples
Find the coordinates of the midpoint of segment XY if X(-2, 3) and Y(-8, -9)

19. Answers
(-5, -3)

20. What about working backwards?
Find the coordinates of D if E(-6, 4) is the midpoint of segment DF and F(-5, -3)

21. Answer Let D be Let E be for the midpoint Let F be So…..
The coordinates for point D are (-7, 11)

22. More Examples
What is the measure of segment PR if Q is the midpoint of segment PR?

23. Answer
If Q is the midpoint then segments PQ and QR are both equal to 6 – 3x
So,
2(6 – 3x) = 14x + 2
12 – 6x = 14x + 2
10 = 20x
x = ½
PR = 14(1/2) + 2 = = 9

24. Last Example
What is the measure of segment AC if B is the midpoint of segment AC?

25. Answer
2(2a – 1) = 3a + 1
4a – 2 = 3a + 1
a = 3
AC = 3(3) + 1
AC = 10