Manipal MET2020MathematicsStraight Lines
If point D divides the base B^ ; of a A B C in the ratio n: m , then the value of m B D^2+n C D^2+(m+n) A D^2 is
Options
- Am A C^2+n A B^2
- B(m+n) (A C^2+A B^2 )
- Cn A C^2+m A B^2
- DNone of the above
Correct answer
C. n A C^2+m A B^2
Step-by-step solution
m B D^2+n C D^2+(m+n) A D^2=m B D^2+n C D^2+m A D^2+n A D^2 aligned & =m (B D^2+A D^2 )+n (C D^2+A D^2 ) & =m (A B^2+2 D M D B )+n (A C^2-2 D M D C ) & =m A B^2+m 2 D M D B+n A C^2-n 2 D M D C & =m A B^2+n A C^2+2 D M(m D B-n D C) & =m A B^2+n A C^2+2 D M(m n-n m) & =m A B^2+n A C^2 aligned