Question
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.
Answers
PsyDAG
Indicate your <I>specific</I> subject in the "School Subject" box, so those with expertise in the area will respond to the question.
Steve
Label the points from left to right: A,P,Q,M,B
AP = 2x
PB = 3x
AQ = 3y
QB = 4y
PQ = 2
AP+PQ=AQ, so AQ-AP=PQ: 3y-2x = 2
PQ+QB=PB, so PB-QB=PQ: 3x-4y = 2
Solving that, we get y=2, so
AB = 7y = 14
AP = 2x
PB = 3x
AQ = 3y
QB = 4y
PQ = 2
AP+PQ=AQ, so AQ-AP=PQ: 3y-2x = 2
PQ+QB=PB, so PB-QB=PQ: 3x-4y = 2
Solving that, we get y=2, so
AB = 7y = 14
Anjana
Answer
Chloe
P divides of the line AB=2:3
Q divides of line AB=3:4
The distance between P and Q=2 cm
we have to find the length of AB=?
AB=AP+PB=2x+3x=5x
Or
AB=AQ+QB=3x+4x=7x
LCM of 5x and 7x=35x=AB
AP+PQ=AQ
2x+2=3x
x=2,
The length of AB=35×2 cm=70 cm
Q divides of line AB=3:4
The distance between P and Q=2 cm
we have to find the length of AB=?
AB=AP+PB=2x+3x=5x
Or
AB=AQ+QB=3x+4x=7x
LCM of 5x and 7x=35x=AB
AP+PQ=AQ
2x+2=3x
x=2,
The length of AB=35×2 cm=70 cm