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What is the ratio in which the line segment joining (2,-3) and (5, 6) is divided by x-axis?

(a) 1:2                    (b) 2:1                       (c) 2:5                       (d) 5:2

This question is similar to Example 9 Chapter 7 Class 10 Coordinate Geometary

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Question 6 What is the ratio in which the line segment joining (2,-3) and (5, 6) is divided by x-axis? (a) 1:2 (b) 2:1 (c) 2:5 (d) 5:2 Let the points be A(2, βˆ’3) & B(5, 6) Let P be the point which divides line segment AB in the ratio k : 1 Since Point P is on xβˆ’axis, ∴ Its y coordinate is 0. So, it is of the form P(x, 0) Finding y coordinate using section formula y = (π‘š_1 𝑦_2 + π‘š_2 𝑦_1)/(π‘š_1+ π‘š_2 ) 0 = (π’Œ Γ—πŸ” + 𝟏 Γ—βˆ’πŸ‘)/(π’Œ + 𝟏) 0 = (6π‘˜ βˆ’3)/(π‘˜ + 1) 0(k + 1) = 6k βˆ’ 3 3 = 6k k = 1/2 Hence the required ratio will be 1/2 : 1 i.e 1 : 2 So, the correct answer is (a)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.