The Midpoint of a Line Segment
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The Midpoint of a Line
Anne Gilleran
undefinedThe Midpoint of a Line
The Midpoint of a Line
The Midpoint of a Line (Warm Up)
The Midpoint of a Line (Warm Up)
+3
+
-2
=
-3
+
-2
=
-3
+
+1
=
+2
+
-3
=
+4
+
-6
=
-5
+
-7
=
-2
+
+8
=
+6
+
-9
=
5.
6.
7.
8.
1.
2.
3.
4.
-2
-12
+6
-3
+1
-5
-2
-1
What’s half way between each pair of numbers?
The Midpoint of a Line
The Midpoint of a Line
?
?
?
?
?
?
?
?
?
?
This is a line…
This is a line segment…
0 1 2 3 4 5 6
5
4
3
2
1
0
y
x
Find the midpoint of the lines between....
a.
(0,1) and (6,5)
b.
(2,6) and (5,2)
Can you write a
formula for co-
ordinates
(x1,y1) and
(x2,y2)
Midpoint at (3,3)
The midpoint of a segment is the average of the
two x co-ordinates and two y co-ordinates.
The midpoint of a line
y
x
(2,5)
(4,2)
x co-ordinate:
y co-ordinate:
=
=
midpoint at ( , )
The midpoint of a line between points
(x
1
,y
1
) and (x
2
,y
2
) is...
The midpoint of a line
y
x
(x
1
,y
1
)
(x
2
,y
2
)
Find the midpoint of
the line segment
between points
(-3,2) and (2,-3)
Midpoint at
Find the midpoint of the line segments between these
sets of points (answer with plickers)
Bonus Questions
Find the centre of a square with co-ordinates at
A (-4,12), B (8,4), C(0,-8) & (12,0)
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?
1.
2.
Midpoint at (-2,-2)
Q1 ANSWER
Meet at
22.5 nautical miles East,
22.5 nautical miles
South
N
E
Q2 ANSWER
0 1 2 3 4 5 6
5
4
3
2
1
0
y
x
Find the midpoint of the line
between (0,5) and (6,1)
Explain how to
find the midpoint
of a line segment
in one sentence.
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(
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,
-
7
)
Explore how to find the midpoint of a line segment through visual aids and practice exercises. Learn the formula for calculating the midpoint between two points on a line. Key points highlight the importance of averaging x and y coordinates. Start mastering geometric concepts with this comprehensive resource.
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Presentation Transcript
The Midpoint of a Line Anne Gilleran
The Midpoint of a Line Learning Intention To learn how to find the midpoint of a line segment
The Midpoint of a Line (Warm Up) +3 + -2 = 5. +4 + -6 = -2 +1 1. -3 + -2 = 6. -5 + -7 = -12 -5 2. -3 + +1 = 7. -2 + +8 = +6 -2 3. +2 + -3 = 8. +6 + -9 = -3 -1 4.
The Midpoint of a Line What s half way between each pair of numbers? 4 ? 8.5 ? 1. 2 & 6 6. 7 & 10 6 ? -7 ? 2. 4 & 8 7. -9 & -5 16 ? -7.5 ? 3. 12 & 20 8. -10 & -5 0 ? -4 ? 4. -3 & 3 9. -11 & 3 2 ? 39 ? 5. -2 & 6 10. 28 & 50
This is a line This is a line segment
Find the midpoint of the lines between.... b. (2,6) and (5,2) a. (0,1) and (6,5) y y 5 4 3 2 1 0 5 4 3 2 1 0 x x 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Can you write a formula for co- ordinates (x1,y1) and (x2,y2) Midpoint at (3,3)
KEY POINT KEY POINT The midpoint of a line The midpoint of a segment is the average of the two x co-ordinates and two y co-ordinates. y 2 + 4 2 = (2,5) x co-ordinate: 5 + 2 2 y co-ordinate: = (4,2) x midpoint at ( , )
KEY POINT KEY POINT The midpoint of a line The midpoint of a line between points y (x1,y1) and (x2,y2) is... (x1,y1) x1+ x2 2 y1+ y2 2 , (x2,y2) x
Find the midpoint of the line segment between points (-3,2) and (2,-3) 3 2 Midpoint at 1 x1+ x2 2 y1+ y2 2 , -3 -2 -1 1 2 3 -1 -2 -3
Find the midpoint of the line segments between these sets of points (answer with plickers) (3,6) 1. (0,3) & (6,5) (6,7) 2. (2,5) & (10,9) (7,11) 3. (8,12) & (6,10) (-4,7) 4. (-3,7) & (-5,7) (3.5,6) 5. (2,2) & (5,10) (0,1) 6. (0,-3) & (0,5) (-6,25) 7. (-7,-10) & (-5,60) (-11.5,-37) 8. (-13,-81) & (-10,7)
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?
Q1 ANSWER Midpoint at (-2,-2) 12 8 4 -12 -8 -4 4 8 12 -4 -8 -12
Q2 ANSWER N Meet at 22.5 nautical miles East, 22.5 nautical miles South E 15 30 45 15 30 45
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 0 x 0 1 2 3 4 5 6
Find the midpoint of the line segment between.... (3,1) & (2,5) (2.5,3)
Find the midpoint of the line segment between.... (2,9) & (6,2) (4,5.5)
Find the midpoint of the line segment between.... (12,8) & (11,18) (11.5,13)
Find the midpoint of the line segment between.... (-2,-3) & (2,3) (0,0)
Find the midpoint of the line segment between.... (-4,-1) & (6,4) (1,1.5)
Find the midpoint of the line segment between.... (-5,-10) & (-3,-4) (-4,-7)
