Worked examples
The question
Question: find the midpoint of (2, 1) and (8, 5).
(2, 1) and (8, 5)
1 Plot the points
Draw the grid.
Put both points on the grid: (2, 1)
and (8, 5).
Join them with a straight line.
We want its middle.
2 Middle of the x's
The midpoint is halfway across.
Halfway between two numbers: add them, then divide by 2.
x = 2 + 82
2 plus 8 is 10.
x = 102
10 divided by 2 is 5.
So x = 5.
x = 5
3 Middle of the y's
Now the y's: the same.
Add them, then divide by 2.
y = 1 + 52
1 plus 5 is 6.
y = 62
6 divided by 2 is 3.
So y = 3.
y = 3
4 The midpoint
So the midpoint is M = (5, 3).
M = (5, 3)
Put M on the grid.
It sits on the line, right in the middle.
5 Check
Let's check on the grid.
From (2, 1) to M:
we go right 3, up 2.
(2, 1) → M: right 3, up 2
From M to the other point:
we go right 3, up 2.
The same moves.
So M is exactly in the middle!
M → (8, 5): right 3, up 2
Let's look back.
First: plot the points.
Then: middle of the x's.
Then: middle of the y's.
Then: the midpoint.
Last: check.
▶ Watch it solved
The question
Question: find the midpoint of (−4, 3) and (2, −2).
(−4, 3) and (2, −2)
1 Plot the points
Draw the grid.
Put both points on the grid: (−4, 3)
and (2, −2).
Join them with a straight line.
We want its middle.
2 Middle of the x's
The midpoint is halfway across.
Halfway between two numbers: add them, then divide by 2.
x = −4 + 22
−4 plus 2 is −2.
x = −22
−2 divided by 2 is −1.
So x = −1.
x = −1
3 Middle of the y's
Now the y's: the same.
Add them, then divide by 2.
y = 3 + (−2)2
Adding a negative is the same as taking away.
+ (−) = −
3 plus −2 is 1.
y = 12
1 divided by 2 is 0.5.
So y = 0.5.
y = 0.5
4 The midpoint
So the midpoint is M = (−1, 0.5).
M = (−1, 0.5)
Put M on the grid.
It sits on the line, right in the middle.
5 Check
Let's check on the grid.
From (−4, 3) to M:
we go right 3, down 2.5.
(−4, 3) → M: right 3, down 2.5
From M to the other point:
we go right 3, down 2.5.
The same moves.
So M is exactly in the middle!
M → (2, −2): right 3, down 2.5
Let's look back.
First: plot the points.
Then: middle of the x's.
Then: middle of the y's.
Then: the midpoint.
Last: check.
▶ Watch it solved
The question
Question: find the other end B, when one end is A = (1, 1) and the midpoint is M = (3, 4).
A = (1, 1) and M = (3, 4)
1 Plot the points
Draw the grid.
Put the end A (1, 1) on the grid
and the midpoint M (3, 4).
2 From A to M
From x = 1 to x = 3 we go right 2.
From y = 1 to y = 4 we go up 3.
3 Same moves again
M is in the middle.
So from M to the other end, the moves are the same: right 2, up 3.
Add the same moves to M: B = (3 + 2, 4 + 3).
B = (3 + 2, 4 + 3)
3 plus 2 is 5.
4 plus 3 is 7.
So B = (5, 7).
B = (5, 7)
Put B on the grid.
4 Check
Let's check: the midpoint of A and B.
The x's: 1 plus 5 is 6.
Half of it is 3.
x = 1 + 52 = 62 = 3
The y's: 1 plus 7 is 8.
Half of it is 4.
We get M = (3, 4) again.
Right!
y = 1 + 72 = 82 = 4
Let's look back.
First: plot the points.
Then: from A to M.
Then: same moves again.
Last: check.
▶ Watch it solved
