Question

Point P partitions the directed segment from A to B into a 1:3 ratio. Q partitions the directed segment from B to A into a 1:3 ratio. Are P and Q the same point? Why or why not?

a)Yes, they both partition the segment into a 1:3 ratio.
b)Yes, they are both the distance from one endpoint to the other.
c)No, P is the distance from A to B, and Q is the distance from B to A.
d)No, Q is closer to A and P is closer to B.

Answer 1

c

Explanation:

bc

Answer 2

c)No, P is the distance from A to B, and Q is the distance from B to A.

Explanation:

Point P partitions the directed segment from A to B into a 1:3 ratio.

Ratio is 1:3

So AP is 1 and PB is 3

Q partitions the directed segment from B to A into a 1:3 ratio.

Ratio is 1:3

So BQ is 1 and QA is 3.

That is AQ= 3 and BQ= 1

The ratio of Q and P varies

AP =1 and AQ=3

So P and Q are not at the same point.

Because P is the distance from A to B and Q is the distance from B to A