Four points `A(6,3),\ B(-3,5),\ C(4,-2)a n d\ D(x ,3x)` are given in such a way that `( Delta D B C)/( Delta A B C)=1/2`,find `x`

Explanation

Given,
`A(6,3),B(−3,5),C(4,−2)`and`D(x,3x)`

Now area of triangle `=(1/2)∣x_1(y_2−y_3)+x_2(y_3−y_2)+x_3(y_1−y_2)∣`

Area of ` triangleDBC =|(((x)(5+2)+(−3)(−2−3x)+4(3x−5))/2)|`

`=|((7x+6+9x+12x−20)/2)|`

`=|((28x−14)/2)|`

Area of `ΔABC =|(((6)(5+2)+(−3)(−2−3)+4(3−5))/2)|`

`=|((42+15−8)/2)|=49/2`

...