If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then

(A) AP =  1/3 AB      (B) AP = PB     (C) PB = 1/3 AB       (D) AP = 1/2 AB

 

This question is inspired from  Example 7 - Chapter 7 Class 10 - Coordinate Geometry

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  1. Chapter 7 Class 10 Coordinate Geometry (Term 1)
  2. Serial order wise

Transcript

Question 15 If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then (A) AP = 1/3 AB (B) AP = PB (C) PB = 1/3 AB (D) AP = 1/2 AB We need to find ratio between AP & PB Let the ratio be k : 1 Also, x1 = 4, y1 = 2 x2 = 8, y2 = 4 & x = 2, y = 1 Using section formula x = (๐‘š1 ๐‘ฅ2 + ๐‘š2 ๐‘ฅ1)/(๐‘š1 + ๐‘š2) 2 = (๐‘˜ ร— 8 + 1 ร— 4)/(๐‘˜ + 1) 2 = (8๐‘˜ + 4)/(๐‘˜ + 1) 2(k + 1) = 8k + 4 2k + 2 = 8k + 4 2 โˆ’ 4 = 8k โˆ’ 2k โˆ’2 = 6k 6k = โˆ’ 2 k = (โˆ’2)/6 k = (โˆ’๐Ÿ)/๐Ÿ‘ Since the ratio is negative, Point P divides AB externally And ratio is 1 : 3 So, our figure looks like Thus, ๐‘จ๐‘ท/๐‘ท๐‘ฉ = ๐Ÿ/๐Ÿ‘ ๐‘จ๐‘ท/(๐‘จ๐‘ท + ๐‘จ๐‘ฉ) = ๐Ÿ/๐Ÿ‘ 3AP = AP + AB 3AP โˆ’ AP = AB 2AP = AB AP = ๐Ÿ/๐Ÿ AB So, the correct answer is (d)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.