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Question

A (6, 3), B (−3, 5), C (4, −2) and D (x, 3x) are four points. If ∆ DBC : ∆ ABC = 1 : 2, then x is equal to
(a) 11/8
(b) 8/11
(c) 3
(d) none of these

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Solution

(a) 118
The area of a triangle with vertices D (x, 3x), B (−3, 5) and C (4, −2) is given below:

Area of ∆DBC = 12x5+2-3-2-3x+43x-5

Area of ∆DBC = 14x-7 sq units

Similarly, the area of a triangle with vertices A (6, 3), B (−3, 5) and C (4, −2) is given below:

∆ABC = 1265+2-3-2-3+43-5

∆ABC = 492sq units

Given:
∆DBC:∆ABC = 1:2

214x-749=128x-4=7x=118

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