Find length of line segment, given P divides AB in ratio 2:3, Q in ratio 3:4, PQ=2

S

sreesuja

New member
Joined
Jul 9, 2012
Messages
4
Points P and Q are both in the line segment AB and on the same side of its midpoint. P
divides AB in the ratio 2 : 3, and Q divides AB in the ratio 3 : 4. If PQ = 2, then find the
length of the line segment AB.
 
sreesuja said:
Points P and Q are both in the line segment AB and on the same side of its midpoint. P
divides AB in the ratio 2 : 3, and Q divides AB in the ratio 3 : 4. If PQ = 2, then find the length of the line segment AB.
Click to expand...
What have you tried or thought about, so far? Where are you stuck?

If you cannot begin, then please answer the following.

Do you understand the meaning of "P divides AB in the ratio 2:3"? What would that division look like, on a diagram of segment AB? In other words, describe how you would use that ratio, to locate point P on a sketch. 8-)
 
sreesuja said:
Points P and Q are both in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2 : 3, and Q divides AB in the ratio 3 : 4. If PQ = 2, then find the length of the line segment AB.
Click to expand...
Draw a horizontal line. Label a point near the left-hand end as "A"; label a point near the right-hand end as "B".

You are given that P splits AB into parts in the ratio 2:3, so there are "five parts", of which two are to the left of P and three are to the right of P.

You are given that Q splits AB into parts in the ratio 3:4, so there are "seven parts", of which three are to the left of Q and four are to the right of Q.

To convert these into comparable "parts", let's split each of the "parts" related to P into seven smaller pieces, so there fourteen pieces to the left of P, and twenty-one pieces to the right of P. And let's split each of the "parts" related to Q into five smaller pieces, so there are fifteen pieces to the left of Q, and twenty pieces to the right of Q. In either case, we have split the line AB into thirty-five pieces, which then must be of equal size (which we can label as "p").

Given the relative numbers of pieces, which of P and Q must be to the left of the other? (That is, what letters should replace the query marks in the following, and in what order?)

Code: 
line:

     (15p) ? ?   (20p)
---*-------*-*----------*---
   A (14p) | | (21p)    B
           | |
           |2|

So where does the segment PQ fall? How then does this segment's length fit in with the other information? Where does this lead?

If you get stuck, please reply showing your work so far. Thank you! ;)
 
You must log in or register to reply here.
Top