One end (2, -1) midpoint (0, 2)

Step by step

The question

Question: find the other end B, when one end is A = (2, −1) and the midpoint is M = (0, 2).

1 Plot the points

Draw the grid.

Put the end A (2, −1) on the grid

and the midpoint M (0, 2).

2 From A to M

From x = 2 to x = 0 we go left 2.

From y = −1 to y = 2 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: left 2, up 3.

Add the same moves to M: B = (0 − 2, 2 + 3).

0 minus 2 is −2.

2 plus 3 is 5.

So B = (−2, 5).

Put B on the grid.

4 Check

Let's check: the midpoint of A and B.

The x's: 2 plus −2 is 0.

Half of it is 0.

The y's: −1 plus 5 is 4.

Half of it is 2.

We get M = (0, 2) again.

Right!

Let's look back.

First: plot the points.

Then: from A to M.

Then: same moves again.

Last: check.