COMEDK2015MathematicsStraight Lines
The medians A D and B E of a triangle with vertices A(0, b), B(0,0) and C(a, 0) are perpendicular to each other, if
Options
- Aa= b 2
- Bb= a 2
- Ca b=1
- Da= 2 b
Correct answer
D. a= 2 b
Step-by-step solution
We have, B E and A D are the medians. So, E and D are the mid-points of A C and B C respectively. Coordinates of E= ( a 2 , b 2 ) and coordinates of D= ( a 2 , 0 ) Now, slope of median B E=m₁= b a Also, slope of median A D=m₂= -2 b a Now, m₁ and m₂ are perpendicular if m₁ m₂=-1 b a (-2 b) a =-1 2 b²=a² a= 2 b