ShmoopTube

00:03

Here’s your shmoop du jour, brought to you by ACDC.

00:06

Not a line segment, but some of their songs had good lines…

00:14

Points A, B, C, D, and E lie on a straight line. C is the midpoint of AE,

00:20

D is the midpoint of CE, and B is the midpoint of AD.

00:25

If AB is equal to 6, what is the length of AE?

00:31

Sometimes…it helps if we sketch out the problem…like we’ve done here.

00:35

We’re also going to label each segment with what fraction of the AE line it is.

00:40

So AC is 1/2 of AE.

00:44

CD is 1/4 of AE.

00:51

AC + CD makes AD, so AD is 1/2 of AE + 1/4 of AE.

00:59

With the addition worked out, AD is 3/4 of AE.

01:02

The problem tells us that AB is 6, and AB + AB is AD because B is the midpoint of AD.

01:09

This means that the length of AD is 12.

01:13

We also know that AD is 3/4 of AE, which allows us to write a short equation.

01:17

3/4 times AE = 12. So multiply both sides by the reciprocal of 3/4…or 4/3.

01:25

…to get that the length of AE is 16.

01:28

And we're done.

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