1. ## Lines?

If A, B, C, and D lie on the same straight line, and if AC = 2CD = 3BD, what is the value of the ratio BC/CD ?

Let AC = 6; then CD = 3, with D on either side of C. BD=2, but B could be on either side of D, and so we have no way of knowing length BC. The value of the ratio BC/CD cannot be determined from the information given.

I don't understand how they came to that conlucsion.

AND why are there 2 D'S?! "D on either side of C"??

2. ## Points on a line

Hello juliak
Originally Posted by juliak
If A, B, C, and D lie on the same straight line, and if AC = 2CD = 3BD, what is the value of the ratio BC/CD ?

Let AC = 6; then CD = 3, with D on either side of C. BD=2, but B could be on either side of D, and so we have no way of knowing length BC. The value of the ratio BC/CD cannot be determined from the information given.

I don't understand how they came to that conlucsion.

AND why are there 2 D'S?! "D on either side of C"??
Have a look at the diagram I've attached.

The question doesn't say that the points A, B, C and D are in that order along the line. They might be in the order A, C, D, B for instance.

So if AC = 6 units and CD = 3, then there are two possible positions for D - one on either side of C. I've called these $D_1$ and $D_2$.

In the same way, for each of the possible positions of D, there are 2 possible positions for B - 4 positions altogether. I've called these $B_1$ through $B_4$.

Do you see why there are several possible answers now?