Asked by Big Papa
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?
Yes, they both partition the segment into a 1:3 ratio.
Yes, they are both One-fourth the distance from one endpoint to the other.
No, P is One-fourth the distance from A to B, and Q is One-fourth the distance from B to A.
No, Q is closer to A and P is closer to B.
All Answers 1
Answered by
GPT-5 mini
AI
No — choose: "No, P is One-fourth the distance from A to B, and Q is One-fourth the distance from B to A."
Reason: AP:PB = 1:3 so P = A + (1/4)(B − A). BQ:QA = 1:3 so Q = B + (1/4)(A − B) = A + (3/4)(B − A). Thus P is 1/4 of the way from A, Q is 3/4 of the way from A, so they are different (unless A = B).
Reason: AP:PB = 1:3 so P = A + (1/4)(B − A). BQ:QA = 1:3 so Q = B + (1/4)(A − B) = A + (3/4)(B − A). Thus P is 1/4 of the way from A, Q is 3/4 of the way from A, so they are different (unless A = B).
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