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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Transcript

Question 19 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 Let point M (2, 6) be Mid-point of A (3p, 4) and B (–2, 2a) Now, Coordinates of mid-point M = ((𝑥_1 + 𝑥_2)/2,(𝑦_1 + 𝑦_2)/2) (2, 6) = ((𝟑𝒑 + (−𝟐) )/𝟐,(𝟒 + 𝟐𝒒)/𝟐) (2, 6) = ((3𝑝 − 2)/2,(2𝑞 + 4)/2) Comparing x-coordinate 2 = (𝟑𝒑 − 𝟐)/𝟐 2 × 2 = 3p − 2 4 = 3p − 2 4 + 2 = 3p 6 = 3p 3p = 6 p = 6/3 p = 2 Comparing y-coordinate 6 = (𝟐𝒒 + 𝟒)/𝟐 6 × 2 = 2q + 4 12 = 2q + 4 12 − 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.