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

Step by step

The question

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

1 Plot the points

Draw the grid.

Put the end A (1, 1) on the grid

and the midpoint M (3, 4).

2 From A to M

From x = 1 to x = 3 we go right 2.

From y = 1 to y = 4 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: right 2, up 3.

Add the same moves to M: B = (3 + 2, 4 + 3).

3 plus 2 is 5.

4 plus 3 is 7.

So B = (5, 7).

Put B on the grid.

4 Check

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

The x's: 1 plus 5 is 6.

Half of it is 3.

The y's: 1 plus 7 is 8.

Half of it is 4.

We get M = (3, 4) again.

Right!

Let's look back.

First: plot the points.

Then: from A to M.

Then: same moves again.

Last: check.