Check sibling questions

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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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 = (𝒎𝟏 𝒙𝟐 + 𝒎𝟐 𝒙𝟏)/(𝒎𝟏 + 𝒎𝟐) 2 = (𝑘 × 8 + 1 × 4)/(𝑘 + 1) 2 = (8𝑘 + 4)/(𝑘 + 1) 2(k + 1) = 8k + 4 2k + 2 = 8k + 4 2 − 4 = 8k − 2k −2 = 6k 6k = − 2 k = (−2)/6 k = (−𝟏)/𝟑 Since the ratio is negative, Point P divides AB externally And ratio is 1 : 3 So, our figure looks like Thus, 𝐴𝑃/𝑃𝐵 = 1/3 𝑨𝑷=𝟏/𝟑 𝑷𝑩 Given options are: (A) AP = 1/3 AB (B) AP = PB (C) PB = 1/3 AB (D) AP = 1/2 AB So, it does not match any of the options 𝐴𝑃/𝑃𝐵 = 1/3 Putting PB = PA + AB 𝑨𝑷/(𝑨𝑷 + 𝑨𝑩) = 𝟏/𝟑 3AP = AP + AB 3AP − AP = AB 2AP = AB AP = 𝟏/𝟐 AB So, the correct answer is (D)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.