Question

Four points A(6,3), B(-3,5), C(4,-2) and D(x,3x) are given such that triangle DBC ratio triangle ABC=1/2, find x?

Answer 1

First, find the area of triangle ABC;  it'll come out to be = -49/2
Then find the area of Triangle DBC by taking co-ordinates of B and C as before, you'll get it's area to be = 14x - 7

now divide them and equate to 1/2

1/2  = (-49/2)/(14x-7)

Now, solve it, x will come out to be -3
Therefore the co-ordinates of point D is =(-3, -9) ;)