Step by step
The question
Question: find the midpoint of (3, −5) and (−1, 1).
1 Plot the points
Draw the grid.
Put both points on the grid: (3, −5)
and (−1, 1).
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.
Adding a negative is the same as taking away.
3 plus −1 is 2.
2 divided by 2 is 1.
So x = 1.
3 Middle of the y's
Now the y's: the same.
Add them, then divide by 2.
−5 plus 1 is −4.
−4 divided by 2 is −2.
So y = −2.
4 The midpoint
So the midpoint is M = (1, −2).
Put M on the grid.
It sits on the line, right in the middle.
5 Check
Let's check on the grid.
From (3, −5) to M:
we go left 2, up 3.
From M to the other point:
we go left 2, up 3.
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.