Check sibling questions

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

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

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Question 19 The mid-point of (3p, 4) and (βˆ’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 = ((π‘₯_1 + π‘₯_2)/2,(𝑦_1 + 𝑦_2)/2) (2, 6) = ((πŸ‘π’‘ + (βˆ’πŸ) )/𝟐,(πŸ’ + πŸπ’’)/𝟐) (2, 6) = ((3𝑝 βˆ’ 2)/2,(2π‘ž + 4)/2) Comparing x-coordinate 2 = (πŸ‘π’‘ βˆ’ 𝟐)/𝟐 2 Γ— 2 = 3p βˆ’ 2 4 = 3p βˆ’ 2 4 + 2 = 3p 6 = 3p 3p = 6 p = 6/3 p = 2 Comparing y-coordinate 6 = (πŸπ’’ + πŸ’)/𝟐 6 Γ— 2 = 2q + 4 12 = 2q + 4 12 βˆ’ 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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.