# Collinear Lengths

Pro Problems > Math > Geometry > Segments## Collinear Lengths

A, B, C, D, and E are, in order, collinear points. The following lengths are known, in terms of x and y:

AB = x - y

AD = x + 2y - 1

BD = AB + 1

DE = 4y - 4

AE = 2x + y

Find the numerical value of the length of AB.

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.## Similar Problems

### A, B, C, and D in a Line

A, B, C, and D are 4 collinear points given in order. The following lengths are known in terms of x and y. Calculate the numerical value of AB.

AB = x - 2y + 17

BC = 2x

CD = y

BD = x + 3y

### Bisect a Segment

A, B, and C are collinear points, with B between A and C. The point M, which is the segment bisector of segment AC, creates segment BM, which has length 3, and segment MC, which has length 11. What are the possible values of the length of AB?

### Segments on a Line

Point A, B, and C are collinear, with A between B and C. The length of AB is half the length of AC, and it is also 20 less than the length of BC. How long are segments BC and AC?