Midpoints

MathsDirect

To find the midpoint of a line joining two points, there is an easy, or a more complicated,( but still easy,) method. First, the more complicated method.

Find the midpoint between (-1,4) and (7,-2)

To move from one point to the other, you move 8 in the x-direction and -6 in the y-direction. Therefore to get to the midpoint, you move (4,-3)

The midpoint is therefore (-1+4,4-3) = (3,1)

How can we write this method down mathematically?

Call the two points
We can therefore calculate
To move from the first point to the midpoint, we must move
So the x co-ordinate is		This is just the average of the two points.
The same is true for y, so the easy way to find the midpoint of
is , the midpoint is

Example

Find the midpoint of (6,5) and (2,-3)

Put the co-ordinates into the formula.

Simplify to find midpoint.

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