Question

Four points A(6,3) , B(-3,5) , C(4,-2) and D(x , 3x) are given in such a way that

ΔDBC/ΔABC = 1/2. Find the value of x.

Answer 1

Step1:- ar (DBC)=1/2 {x (5+2)-3 (-2-3x)+4 (3x-5)}=1/2 (7x+6+9x+12x-20)=1/2 (28x-14)
=14x-7
step 2:- ar (ABC)=1/2 {6 (5+2)-3 (-2-3)+4 (3-5)}=1/2 (42+15-8)=49/2
step 3:-
=> ar (DBC)/ar (ABC)=1/2
=> (14x-7)/49/2=1/2
=> 14x-7=49/4
=> 14x=77/4
=> x=11/8