The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at

(A) (0, 13)      (B) (0, –13)     (C) (0, 12)      (D) (13, 0)

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Question 17 The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at (A) (0, 13) (B) (0, –13) (C) (0, 12) (D) (13, 0) Let Line l be the perpendicular bisector of AB Let line l meet y-axis at point P Since point P is in y-axis ∴ Coordinates of P = (0, y) By symmetry AP = BP √(( 0 −1)2+(𝑦−5)2) = √(( 0 −4)2+(𝑦−6)2) √((−1)2+(𝑦−5)2) = √(( −4)2+(𝑦−6)2) √(1+𝑦^2+25−10𝑦) = √(16+𝑦^2+36−12𝑦) √(𝑦^2−10𝑦+26) = √(𝑦^2−12𝑦+52) Squaring both sides (√(𝑦^2−10𝑦+26) )^2 = (√(𝑦^2−12𝑦+52) )^2 𝑦^2−10𝑦+26 = 𝑦^2−12𝑦+52 −10𝑦+26 = −12𝑦+52 12𝑦−10𝑦 = 52−26 2𝑦=26 𝑦=26/2 𝒚=𝟏𝟑 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.