How to find the Midpoint between two (x,y) coordinates.

1. Midpoint Between
Points
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2. The 90 mile straight section of highway lies between the
towns of Balladonia and Caiguna in the Australian Outback.
Some friends of ours recently drove this stretch of the Eyre
Highway.
If their car started making some strange noises along this
section of road, would they be better off heading back to
Balladonia, or continuing onto Caiguna?
Well assuming there is a mechanic in each town, it would
depend on whether or not they had crossed the halfway point
(or "Midpoint") of their journey.
Midpoint Between
Points

3. 90
We need to find the
Midpoint between
Balladonia at (0,2)
and
Calguna at (90,2).
Eg. We need to halve
90, and we get 45 miles
OR We can add the
x-coords and halve,
eg. (0+90)/2 = 45 miles
B C
Midpoint Between
Points
0

4. 5
-5
We need to find the
Midpoint between
Point A at (-2,-2)
and
Point B at (2,6)
We measure Across,
and we measure Up,
and work out the
halfway point is at
x = 0, y = 2 or (0,2)
A
B
Across = 4 squares
Midpoint is 2 squares
across at x = 0
Up = 8 Squares
Midpoint is 4
squares up at
y = 2
Midpoint Between
Points

5. 5
-5
A (3, -2)
B (-3,4)
-3
Midpoint of Points
Example
We need to find the
Midpoint between
Point A at (3,-2)
and
Point B at (-3,4)
Measure Across & Halve,
and measure Up & Halve,
and thereby work out the
halfway point is at the pt
x = __, y = __ or (__,__)

6. 5
-5
A (3, -2)
B (-3,4)
Midpoint of Points
Example
We need to find the
Midpoint between
Point A at (3,-2)
and
Point B at (-3,4)
Measure Across & Halve,
and measure Up & Halve,
and thereby work out the
halfway point is at the pt
x = 0, y = 1 or (0,1)
Across = 6 squares
Midpoint is 3 squares
across at x = 0
Up = 6 Squares
Midpoint is 3
squares up at
y = 1

7. 5
-5
To find the Midpoint
between two points:
Point A and Point B
The midpoint is (x,y)
where :
x = (x1 + x2 ) / 2 and
y = (y1 + y2 ) / 2
A
Midpoint Formula
B (x2,y2)
A (x1,y1)
M (x,y)

8. 5
-5
A (-2,-2)
•Label the Points as A and B
•Label A (x1,y1) and B (x2,y2)
•Substitute the Values of
(x1,y1) and (x2,y2) numbers
into the Midpoint Formula:
(X1+X2) / 2 and (Y1+Y2) / 2
•Calculate and write as (x,y)
Midpoint Formula
STEPS
B (2,6)
A (x1,y1)
B (x2,y2)

9. 5
-5
A (-2,-2)
• Substitute the Values of
(x1,y1) and (x2,y2) numbers
into the Midpoint Formula:
(X1+X2) / 2 and (Y1+Y2) / 2
=(__+__) / 2 and (__+__) / 2
= ____ and _____
= ( ___ , ___)
Midpoint Formula Example
1
B (2,6)
A (x1,y1)
B (x2,y2)

10. 5
-5
A (-2,-2)
• Substitute the Values of
(x1,y1) and (x2,y2) numbers
into the Midpoint Formula:
(X1+X2) / 2 and (Y1+Y2) / 2
=(-2+2) / 2 and (-2+6) / 2
= 0 and 2
= (0 , 2)
Midpoint Formula Example
1
B (2,6)
A (x1,y1)
B (x2,y2)
M (0,2)

11. 5
-5
A (-2,-2)
Add the Points and Divide
the Answer by two.
(-2 , -2)
+ ( 2 , 6)
( 0 , 4)
= (0 , 2)
Example 1 Alternative
Method
B (2,6)
M (0,2)
Divide by 2
Add

12. 5
-5
A (__,__)
B (__,__)
-3
Midpoint Formula Example
2
• Substitute the Values of
(x1,y1) and (x2,y2) numbers
into the Midpoint Formula:
(X1+X2) / 2 and (Y1+Y2) / 2
=(__+__) / 2 and (__+__) / 2
= ____ and _____
= ( ___ , ___)

13. 5
-5
A (3,-2)
B (-4,4)
-3
Midpoint Formula Example
2
• Substitute the Values of
(x1,y1) and (x2,y2) numbers
into the Midpoint Formula:
(X1+X2) / 2 and (Y1+Y2) / 2
=(3+-4) / 2 and (-2+4) / 2
= -0.5 and 1
= ( -0.5 , 1)
A (x1,y1)
B (x2,y2)
M (-0.5, 1)

14. 5
-5
A (3,-2)
B (-4,4)
-3
Example 2 Alternative Method
M (-0.5, 1)
Add the Points and Divide
the Answer by two.
( 3 , -2)
+ (-4 , 4)
(-1 , 2)
= (-0.5 , 1)
Divide by 2
Add

15. Blank X-Y Grid
-3 3
5
-5

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