MATH 8

MIDPOINT

What’s a midpoint?

A MIDPOINT is a point that divides a line segment into two equal length parts.

MIDPOINT

How can we find its location?

We can find the location of a midpoint ifwe are given the coordinates of the

segment’sendpoints?WAIT-What’s an endpoint?

An endpoint is where a segment either starts or ends.

Endpoint Endpoint

Alright, now how do we find it?

It’s simple…. Even an 8th grader could do it!

All you need to know is the formula!

I know, you want to know what the formula is………

Well, think about it, how do we cut something into two parts? What operation would we use?

We can’t wait any longer….

YES, division!!!!!!

Alright, here’s the formula….

€

x1 + x2

2,y1 + y2

2

⎛

⎝ ⎜

⎞

⎠ ⎟

Huh?!?!?!?!

I suppose you want an example of how to use the formula now?

Here are the coordinates of the endpoints of a segment: (6, 3) and (2, -4)

We need to determine which is our point 1 and which is our point 2 (THIS SHOULD SOUND FAMILIAR).

Show me more!!!!

Let’s label our points:(6, 3) and (2, -4)

Now, let’s re-write the formula:

Substitute our values in and do the math!!!!!

€

x1,y1( )

€

x2,y2( )

€

x1 + x2

2,y1 + y2

2

⎛

⎝ ⎜

⎞

⎠ ⎟

€

6 + 2

2,3 + −4

2

⎛

⎝ ⎜

⎞

⎠ ⎟

ALMOST FINISHED!!!!

Add the numerators!

Simplify the fractions!€

6 + 2

2,3 + −4

2

⎛

⎝ ⎜

⎞

⎠ ⎟

€

8

2,−1

2

⎛

⎝ ⎜

⎞

⎠ ⎟

€

4,−1

2

⎛

⎝ ⎜

⎞

⎠ ⎟

FINISHED!

THE END