1. The Midpoint of a Line
Anne Gilleran

2. The Midpoint of a Line
To learn how to find the midpoint of a line segment
Learning Intention

3. The Midpoint of a Line (Warm Up)1. = +1 5. = -2 2. = -5 6. =
-12 3. = -2 7. = +6 4. = -1 8. = -3 3

4. The Midpoint of a Line What’s half way between each pair of numbers?1.
2 & 6 4 6.
7 & 10
8.5 2.
4 & 8 6 7.
-9 & -5 -7 3.
12 & 20 16 8.
-10 & -5
-7.5 4.
-3 & 3 9.
-11 & 3 -4 5.
-2 & 6 2
10.
28 & 50 39 ? ? ? ? ? ? ? ? ? ? 4

5. This is a line…
This is a line segment…

6. x x Find the midpoint of the lines between.... y y b. (2,6) and (5,2)
a. (0,1) and (6,5)
b. (2,6) and (5,2) 5 4 3 2 1 y x y 5 4 3 2 1 x
Can you write a formula for co-ordinates (x1,y1) and (x2,y2)
Midpoint at (3,3)

7. The midpoint of a line x KEY POINT y midpoint at ( , )
The midpoint of a segment is the average of the two x co-ordinates and two y co-ordinates. y 2
x co-ordinate: =
(2,5) 2
y co-ordinate: =
(4,2)
copy down x
midpoint at ( , )

8. The midpoint of a line x KEY POINT y
The midpoint of a line between points
(x1,y1) and (x2,y2) is... y
(x1,y1)
x1 + x2 2
y1 + y2 ,
(x2,y2)
copy down x

9. Find the midpoint of the line segment between points
(-3,2) and (2,-3) 1 2 3 -1 -2 -3
Midpoint at
x1 + x2 2
y1 + y2 ,

10. Find the midpoint of the line segments between these sets of points (answer with plickers)1.
(0,3)
&
(6,5)
(3,6) 2.
(2,5)
(10,9)
(6,7) 3.
(8,12)
(6,10)
(7,11) 4.
(-3,7)
(-5,7)
(-4,7) 5.
(2,2)
(5,10)
(3.5,6) 6.
(0,-3)
(0,5)
(0,1) 7.
(-7,-10)
(-5,60)
(-6,25) 8.
(-13,-81)
(-10,7)
(-11.5,-37)

11. Bonus Questions 1. Find the centre of a square with co-ordinates at
A (-4,12), B (8,4), C(0,-8) & (12,0) 2.
Two boats begin at the same place. One sails East at 15 nautical miles per hour, the other sails South at the same speed. After 3 hours they turn & begin sailing toward each other.
Where do they meet in relation to where they first started?

12. Q1 ANSWER 4 8 12 -4 -8
-12
Midpoint at (-2,-2)

13. N E Meet at 22.5 nautical miles East, 22.5 nautical miles South
Q2 ANSWER N 15 30 45
Meet at
22.5 nautical miles East,
22.5 nautical miles South E

14. Find the midpoint of the line between (0,5) and (6,1)
PLENARY
Find the midpoint of the line between (0,5) and (6,1) y
Explain how to find the midpoint of a line segment in one sentence. 5 4 3 2 1 x

15. On mini
whiteboards

16. Find the midpoint of the line segment between....
(3,1) & (2,5)
(2.5,3)

17. Find the midpoint of the line segment between....
(2,9) & (6,2)
(4,5.5)

18. Find the midpoint of the line segment between....
(12,8) & (11,18)
(11.5,13)

19. Find the midpoint of the line segment between....
(-2,-3) & (2,3)
(0,0)

20. Find the midpoint of the line segment between....
(-4,-1) & (6,4)
(1,1.5)

21. Find the midpoint of the line segment between....
(-5,-10) & (-3,-4)
(-4,-7)