1. Lesson 1 – 3 Distance and Midpoints
Geometry
Lesson 1 – 3
Distance and Midpoints
Objective:
Find the distance between two points.
Find the midpoint of a segment.

2. Distance: on a number line
Distance formula (on a number line)
The absolute value of the difference between their points.

3. Use the number line to find the followingAC CF FB

4. Distance: On the coordinate plane
Distance formula (on a coordinate plane)

5. Example Find the distance between C (-4, -6) & D(5, -1)
Doesn't matter in which order
You subtract x’s or y’s.
Radical is already simplified.
Write answer as both radical and decimal

6. Find the distance
E (-5, 6) & F (8, -4)
J (4, 3) & K (-3, -7)

7. Midpoint: On a number line
Midpoint is the point halfway between the endpoints of the segment.
Take the average of the numbers or
just add up the numbers divide by 2.

8. Example
Find the midpoint between 15 inches and 37.5 inches.

9. Example
The temperature on a thermometer dropped from a reading of 25 degrees to -8 degrees. Find the midpoint of these temperatures.
M = (25 – 8) / 2
M = 17 / 2
M = 8.5 degrees

10. Midpoint: On coordinate plane
Average of both the x’s and y’s

11. Example
Find the coordinates of M, the midpoint of ST, for S (-6, 3) & T (1, 0).
Make a visual (helpful for later)
S (-6,3)
M (? , ?)
T (1, 0)

12. Example
Find the midpoint
A (5, 12) B(-4, 8)
C (-8, -2) D (5, 1)

13. Find the coordinate of the endpoint
Find the coordinates of J, if K (-1, 2) is the midpoint of JL and L (3, -5).
Make a visual
J (?, ?) K (-1, 2) L (3, -5)
K is the midpoint so when I add the x’s and / 2 should = -1
J (-5, 9)
(2)
(2)
(2)
(2)
Check it:
(-5 + 3) / 2 = -1
(9 – 5) / 2 = 2
x + 3 = -2
y – 5 = 4
x = -5
y = 9

14. Find the Endpoint G (-2, 14) y = 14 x = -2
Find the coordinates of the missing endpoint if P is the midpoint of EG E (-8, 6), P (-5, 10)
E (-8, 6) P (-5, 10) G (x, y)
G (-2, 14)
6 + y = 20
-8 + x = -10
y = 14
x = -2

15. Example
Find the coordinates of the missing endpoint if P is the midpoint of EG P (-1, 3), E (5, 6)
G (-7, 0)
x + 5 = -2
y + 6 = 6
y = 0
x = -7

16. Find the measure PQ = 9y – 2 = 9(4) – 2 = 34
Find the measure of PQ if Q is the midpoint of PR.
9y – 2 = y
4y – 2 = 14
4y = 16
y = 4
PQ = 9y – 2 = 9(4) – 2 = 34

17. Your Turn
Find the measure of YZ if Y is the midpoint of XZ and XY = 2x – 3 and YZ = 27 – 4x
2x – 3 = 27 – 4x
6x – 3 = 27
6x = 30
x = 5
YZ = 27 – 4(5) = 27 – 20 = 7

18. Your Turn 2(4x + 5) = 78 or 4x + 5 = 78/2 4x + 5 = 39 4x = 34
Find the value of x if C is the midpoint of AB, AC = 4x + 5 and AB = 78.
2(4x + 5) = or 4x + 5 = 78/2
**AB is the whole segment
4x + 5 = 39
4x = 34
x = 8.5

19. Bisector Segment bisector
Any segment, line, or plane that intersects a segment at its midpoint