Modern Geometry

Question

Find the value if AC = 3y + 5. CB = 4y - 1, AB= 9y - 12, and point C is between A & B.

Answer 1

If C is "between" A and B, it means that they are all on the same line.

 

So AC + CB must equal AB.

 

That means that 3y + 5 + 4y - 1 = 9y - 12.  That's an equation that can be solved:

 

3y + 5 + 4y - 1 = 9y - 12

7y + 4 = 9y - 12

7y + 16 = 9y

16 = 2y

8 = y.

 

Once you have y, you can find all the lengths.

 

Answer 2

We know from the problem that A,B, and C are collinear because the problem states that C is between A and B.  

 

We use segment addition postulate 

 

AC+CB=AB

 

by substitution 

(3y+5)+(4y-1)=9y-12

 

7y+4=9y-12

2y=16

y=8

therefore AC=29   CB=31   and AB=60