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1. Let P,Q, and X be three distinct collinear points and X is between P and Q. (a) If 0 < t < 1 and X = (1 t)P+tQ, show that d(PX) = d(X,Q) 1t. (b) Use the result in (a) to find the point X that divides the segment PQ in the ratio r: s. Illustrate using r = 2, s = 3, P = (-3,5), Q = (8,4).

1. Let P,Q, and X be three distinct collinear points and X is between P and Q. (a) If 0 < t < 1 and X = (1 t)P+tQ, show that d(PX) = d(X,Q) 1t. (b) Use the result in (a) to find the point X that divides the segment PQ in the ratio r: s. Illustrate using r = 2, s = 3, P = (-3,5), Q = (8,4).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Let P,Q, and X be three distinct collinear points and X is between P and Q. (a) If 0 < t < 1 and X = (1 t)P+tQ, show that d(PX) = d(X,Q) 1t. (b) Use the result in (a) to find the point X that divides the segment PQ in the ratio r: s. Illustrate using r = 2, s = 3, P = (-3,5), Q = (8,4).
Transcribed Image Text:1. Let P,Q, and X be three distinct collinear points and X is between P and Q. (a) If 0 < t < 1 and X = (1 t)P+tQ, show that d(PX) = d(X,Q) 1t. (b) Use the result in (a) to find the point X that divides the segment PQ in the ratio r: s. Illustrate using r = 2, s = 3, P = (-3,5), Q = (8,4).
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