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Misc 17 - Hypotenuse of a right angled triangle has its ends at - Miscellaneous

Misc 17 - Chapter 10 Class 11 Straight Lines - Part 2
Misc 17 - Chapter 10 Class 11 Straight Lines - Part 3
Misc 17 - Chapter 10 Class 11 Straight Lines - Part 4

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Misc 17 The hypotenuse of a right angled triangle has its ends at the points (1, 3) and ( 4, 1). Find an equation of the legs (perpendicular sides) of the triangle. Let ABC be a right angle triangle where AC is the hypotenuse & B = 90 Given that the hypotenuse has its ends at points (1, 3) & ( 4, 1) A = (1, 3) & C = ( 4, 1) We need to calculate equations of the legs of triangle i.e. we need to find equation of line AB & BC Let Slope of line AB = m We know if two lines are perpendicular, then product of their slope is 1 Here, AB & BC are perpendicular Slope of AB Slope of BC = 1 m Slope of BC = 1 Slope of BC = ( 1)/ Now, We know that equation of line having slope m and passing through point (x1,y1) is y y1 = m(x x1) Equation of line AB passing through point A(1, 3) & having slope m is (y 3) = m(x 1) Similarly, Equation of line BC passing through point C( 4, 1) & having slope ( 1)/ is (y 1) = ( 1)/ (x (-4)) (y 1) = ( 1)/ (x + 4) We can have any value of m Finding equation of legs of triangle (AB & BC) by taking specific value of m For m = 0 Equation of AB (y 3) = m(x 1) y 3 = 0(x 1) y 3 = 0 y = 3 Equation BC y 1 = ( 1)/ (x + 4) y 1 = ( 1)/0 (x + 4) 0(y 1) = 1(x + 4) 0 = x 4 x = 4

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Davneet Singh

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.