CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [MCQ]

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Question 43 (Case Based Question) - CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [MCQ] - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by

 The fault line 3x + y – 9 = 0 divides the line joining the Country P(1, 3) and Country Q(2, 7) internally in the ratio

(a) 3 : 4   (b) 3 : 2   (c) 2 : 3   (d) 4 : 3

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Transcript

Question 43 The fault line 3x + y – 9 = 0 divides the line joining the Country P(1, 3) and Country Q(2, 7) internally in the ratio (a) 3 : 4 (b) 3 : 2 (c) 2 : 3 (d) 4 : 3 Using section formula x = (𝒎𝟏 𝒙𝟐 + 𝒎𝟐 𝒙𝟏)/(𝒎𝟏 + 𝒎𝟐) x = (𝑘 × 2 + 1 × 1)/(𝑘 + 1) x = (𝟐𝒌 + 𝟏)/(𝒌 + 𝟏) y = (𝒎𝟏 𝒚𝟐 + 𝒎𝟐 𝒚𝟏)/(𝒎𝟏 + 𝒎𝟐) y = (𝑘 × 7 + 1 × 3)/(𝑘 + 1) y = (𝟕𝒌 + 𝟑)/(𝒌 + 𝟏) Since point Z lies on line It will satisfy it’s equation Putting values of x and y in equation 3x + y − 9 = 0 𝟑((𝟐𝒌+ 𝟏)/(𝒌 + 𝟏))+(𝟕𝒌 + 𝟑)/(𝒌 + 𝟏) − 9 = 0 (3(2𝑘+ 1))/(𝑘 + 1)+(7𝑘 + 3)/(𝑘 + 1) − 9 = 0 (6𝑘 + 3)/(𝑘 + 1)+(7𝑘 + 3)/(𝑘 + 1) − 9 = 0 (6𝑘 + 3 + 7𝑘 + 3)/(𝑘 + 1) − 9 = 0 (13𝑘 + 6)/(𝑘 + 1) − 9 = 0 (13𝑘 + 6 − 9(𝑘 + 1))/(𝑘 + 1) = 0 (13𝑘 + 6 − 9𝑘 − 9)/(𝑘 + 1) = 0 (𝟒𝒌 − 𝟑)/(𝒌 + 𝟏) = 0 4k − 3 = 0 4k = 3 k = 𝟑/𝟒 ∴ Required ratio is 3 : 4 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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.