Question

Four points A (6, 3), B (−3, 5), C(4, −2) and D (x, 3x) are given in such a way that $\frac{∆DBC}{∆ABC}=\frac{1}{2},$find x.

Answer 1

GIVEN: four points A (6, 3), B (−3, 5) C (4, −2) and D(x, 3x) such that

TO FIND: the value of x

PROOF:

We know area of the triangles formed by three points is given by

Now

Area of triangle DBC taking D(x, 3x), B (−3, 5), C (4, −2)

Area of triangle ABC taking, A (6, 3), B (−3, 5), C (4, −2)

Also it is given that

Substituting the values from (1) and (2) we get