The mid-point of (3p, 4) and (−2, 2q) is (2, 6) . Find the value of p + q

(a) 5  (b) 6        (c) 7        (d) 8

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  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

Question 19 The mid-point of (3p, 4) and (โˆ’2, 2q) is (2, 6) . Find the value of p + q (a) 5 (b) 6 (c) 7 (d) 8 Let point M (2, 6) be Mid-point of A (3p, 4) and B (โ€“2, 2a) Now, Coordinates of mid-point M = ((๐‘ฅ_1 + ๐‘ฅ_2)/2,(๐‘ฆ_1 + ๐‘ฆ_2)/2) (2, 6) = ((๐Ÿ‘๐’‘ + (โˆ’๐Ÿ) )/๐Ÿ,(๐Ÿ’ + ๐Ÿ๐’’)/๐Ÿ) (2, 6) = ((3๐‘ โˆ’ 2)/2,(2๐‘ž + 4)/2) Comparing x-coordinate 2 = (๐Ÿ‘๐’‘ โˆ’ ๐Ÿ)/๐Ÿ 2 ร— 2 = 3p โˆ’ 2 4 = 3p โˆ’ 2 4 + 2 = 3p 6 = 3p 3p = 6 p = 6/3 p = 2 Comparing y-coordinate 6 = (๐Ÿ๐’’ + ๐Ÿ’)/๐Ÿ 6 ร— 2 = 2q + 4 12 = 2q + 4 12 โˆ’ 4 = 2q 8 = 2q 2q = 8 q = 8/2 q = 4 Thus, p + q = 2 + 4 = 6 So, the correct answer is (b)

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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.