Point P partitions the directed segment from A to B into 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?

Point Q is further from A than point P, therefore, they are not the same point

Step-by-step explanation:

The given information are;

Point P partitions the directed segment from A → B into the ratio of 1:3

Point Q partitions the directed segment from B → A into the ratio of 1:3

We note that the properties of a directed segment are that it has a length and direction with a defined starting or initial point.

Hence the two segments when arranged in the same direction are;

A B and B A

Hence point P is at a the point 1/(1 + 3) or 1/4 of AB or 1/4 times the length of AB from A

Point Q is at a the point  1/4 of B/A or 1/4 times the length of AB from B which is 3/4 times the length of AB from A

Therefore, point Q is further from A than point P which means they are not the same point.

step-by-step explanation:

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

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