Step by step
The question
Question: find the midpoint of (1, 5) and (7, −3).
1 Plot the points
Draw the grid.
Put both points on the grid: (1, 5)
and (7, −3).
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.
1 plus 7 is 8.
8 divided by 2 is 4.
So x = 4.
Is 4 really in the middle?
From 1, a jump of 3 gives 4.
From 4, 3 more gives 7.
The same jump from each end.
So adding and halving finds the middle.
3 Middle of the y's
Now the y's: the same.
Add them, then divide by 2.
Adding a negative is the same as taking away.
5 plus −3 is 2.
2 divided by 2 is 1.
So y = 1.
4 The midpoint
So the midpoint is M = (4, 1).
Put M on the grid.
It sits on the line, right in the middle.
5 Check
Let's check on the grid.
From (1, 5) to M:
we go right 3, down 4.
From M to the other point:
we go right 3, down 4.
The same moves.
So M is exactly in the middle!
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.