Midpoint (1, 2) one end (-3, 4)

Step by step

The question

Question: find the other end B, when one end is A = (−3, 4) and the midpoint is M = (1, 2).

1 Plot the points

Draw the grid.

Put the end A (−3, 4) on the grid

and the midpoint M (1, 2).

2 From A to M

From x = −3 to x = 1 we go right 4.

From y = 4 to y = 2 we go down 2.

3 Same moves again

M is in the middle.

So from M to the other end, the moves are the same: right 4, down 2.

Add the same moves to M: B = (1 + 4, 2 − 2).

1 plus 4 is 5.

2 minus 2 is 0.

So B = (5, 0).

Put B on the grid.

4 Check

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

The x's: −3 plus 5 is 2.

Half of it is 1.

The y's: 4 plus 0 is 4.

Half of it is 2.

We get M = (1, 2) again.

Right!

Let's look back.

First: plot the points.

Then: from A to M.

Then: same moves again.

Last: check.