Midpoint (-2, 1) (4, 5)

Step by step

The question

Question: find the midpoint of (−2, 1) and (4, 5).

1 Plot the points

Draw the grid.

Put both points on the grid: (−2, 1)

and (4, 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.

−2 plus 4 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.

1 plus 5 is 6.

6 divided by 2 is 3.

So y = 3.

4 The midpoint

So the midpoint is M = (1, 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.

From M to the other point:

we go right 3, 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.