Last updated at May 29, 2018 by Teachoo

Transcript

Ex 10.3, 13 Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2). Let AB be the line joining points A(−1, 2) & B(3, 4) Let CD be the right bisector of line AB We have to find equation of line CD Since CD is the right bisector of line AB, Point P is the mid-point of line AB We know that co-ordinates of mid-point is given by ((𝑥1 + 𝑥2)/2, (𝑦1 + 𝑦2)/2) So, co-ordinates of point P = (( − 1 + 3)/2, (2 + 4)/2) = (2/2 " , " 6/2) = (1, 3) Since CD is the right bisector of line AB ∴ Line CD ⊥ line AB And, we know that if two lines are perpendicular, their product of slope is –1 So, Slope of CD × Slope of AB = − 1 Slope of CD = ( − 1)/(𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝐴𝐵) Finding slope of line AB Slope of a line joining points (x1,y1) & (x2,y2) is = (𝑦_2 − 𝑦_1)/(𝑥_2 − 𝑥_1 ) Slope of AB joining (3, 4)& ( − 1, 2) = (2 − 4)/( − 1 − 3) = (2 − 4)/( − 1 − 3) = ( − 2)/( − 4) = 1/2 So, Slope of AB = 1/2 ∴ Slope of CD = ( − 1)/(𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝐴𝐵) = ( − 1)/(1/2) = − 2 We know that equation of a line passes through (x1, y1) & having slope of m is (y − y1) = m(x − x1) Equation of line CD passing through point P(1, 3) & slope of –2 is (y – 3) = –2 (x – 1) y – 3 = –2x + 2 y + 2x = 2 + 3 2x + y = 5 Thus, 2x + y − 5 = 0 is the required equation.

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.