Midpoint (4, 0) one end (6, -3)

Step by step

The question

Question: find the other end B, when one end is A = (6, −3) and the midpoint is M = (4, 0).

1 Plot the points

Draw the grid.

Put the end A (6, −3) on the grid

and the midpoint M (4, 0).

2 From A to M

From x = 6 to x = 4 we go left 2.

From y = −3 to y = 0 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 = (4 − 2, 0 + 3).

4 minus 2 is 2.

0 plus 3 is 3.

So B = (2, 3).

Put B on the grid.

4 Check

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

The x's: 6 plus 2 is 8.

Half of it is 4.

The y's: −3 plus 3 is 0.

Half of it is 0.

We get M = (4, 0) again.

Right!

Let's look back.

First: plot the points.

Then: from A to M.

Then: same moves again.

Last: check.