Check sibling questions

Ex 10.1, 6 - Without using Pythagoras theorem, show - Slope - Prependicularity

Ex 10.1, 6 - Chapter 10 Class 11 Straight Lines - Part 2
Ex 10.1, 6 - Chapter 10 Class 11 Straight Lines - Part 3 Ex 10.1, 6 - Chapter 10 Class 11 Straight Lines - Part 4


Transcript

Ex10.1, 6 Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle. Let the 3 points of triangle be A (4, 4) , B (3, 5) , C (–1, –1) Lets calculate slope of AB, BC and AC If product of slope is -1 It means lines are perpendicular and it is a right angle triangle Slope of AB A (4, 4) , B (3, 5) Here, x1 = 4, y1 = 4 x2 = 3, y2 = 5 Putting values Slope of AB = (5 − 4)/(3 − 4) = 1/( − 1) = -1 Slope of BC B (3, 5) , C (–1, –1) Here, x1 = 3, y1 = 5 x2 = -1, y2 = -1 Putting values Slope of BC = ( − 1 − (5))/( − 1 − 3) = ( − 6)/( − 4) = 3/2 Slope of AC A (4, 4) , C (–1, –1) Here, x1 = 4, y1 = 4 x2 = –1, y2 = –1 Putting values Slope of AC = ( − 1 − 4)/( − 1 − 4) = ( − 5)/( − 5) = 1 Now, Slope of AB × Slope of AC = (-1) × (1) = -1 Since product of slope is –1 ∴ Lines AB & AC are perpendicular Hence it is right-angled triangle

Davneet Singh's photo - Co-founder, Teachoo

Made by

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.