Step by step
The question
Question: find the midpoint of (−2, 3) and (6, 7).
1 Plot the points
Draw the grid.
Put both points on the grid: (−2, 3)
and (6, 7).
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.
−2 plus 6 is 4.
4 divided by 2 is 2.
So x = 2.
Is 2 really in the middle?
From −2, a jump of 4 gives 2.
From 2, 4 more gives 6.
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.
3 plus 7 is 10.
10 divided by 2 is 5.
So y = 5.
4 The midpoint
So the midpoint is M = (2, 5).
Put M on the grid.
It sits on the line, right in the middle.
5 Check
Let's check on the grid.
From (−2, 3) to M:
we go right 4, up 2.
From M to the other point:
we go right 4, up 2.
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.