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The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the

(A) I quadrant   (B) II quadrant

(C) III quadrant   (D) IV quadrant

 

This question is inspired from  Question 8 - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

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Question 12 The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the (A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant Let points be A (7, –6) and B (3, 4) Let point be P(x, y) divide AB in ratio 1 : 2 Coordinates of P = ((𝑚_1 𝑥_2 + 𝑚_2 𝑥_1)/(𝑚_1 + 𝑚_2 ), (𝑚_1 𝑦_2 + 𝑚_2 𝑦_1)/(𝑚_1 + 𝑚_2 )) = ((1 × 3 + 2 × 7)/(1 + 2), (1 × 4 + 2 × (−6))/(1 + 2)) = ((3 + 14)/3, (4 − 12)/3) = (𝟏𝟕/𝟑, (−𝟖)/𝟑) Since x is positive, y is negative The point lies in 4th Quadrant So, the correct answer is (d)

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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.