10/12/2014 The Midpoint Formula - Geometry - Free Math Help 2011

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The Midpoint FormulaWhat is the midpoint formula? It's an algebraic tool to find the point halfway between two otherpoints. If you imagine a line between those two points, the midpoint lies exactly halfway along theline. Mathematically, you would say that it is equidistant from both points and lies on the lineconnecting those two points.

So, what IS the midpoint formula? Here you go:

And what does it tell you? Imagine you have two points. X1 represents the x-coordinate of the firstpoint, and X2 represents the x-coordinate of the second point. Since you're dividing by 2, you'rereally just taking the average. The same applies for the y-coordinates.

So what, I'm just taking the average? Yup! The midpoint between two points is just the average of thex-coordinates and the average of the y-coordinates.

Let's look at a quick example if you're not clear yet:

Example 1:

Find the point halfway between (0,3) and (4,7):

Remember the midpoint formula:

Plug in the appropriate values:

And simplify for your solution:

Interactive problem solver:

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