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

area of triangle DBC/area of triangle ABC =1/2. Find x

Question

Four points A(6,3) , B(-3,5) , C(4,-2) , and D(x,3x) are given
in such a way that
area of triangle DBC/area of triangle ABC =1/2 Find x

Ajanta Trivedi · Accepted Answer

the given coordinates of the points are A(6,3) , B(-3,5) , C(4,-2) , and D(x,3x)

therefore the area of the triangle ABC is

$a r e a (A B C) = \frac{1}{2} [6 (5 + 2) - 3 (- 2 - 3) + 4 (3 - 5)] = \frac{1}{2} [6 * 7 - 3 * (- 5) + 4 (- 2)] = \frac{1}{2} [42 + 15 - 8] = \frac{1}{2} [49]$

$a r e a (D B C) = \frac{1}{2} [x (5 + 2) - 3 (- 2 - 3 x) + 4 (3 x - 5)] = \frac{1}{2} [7 x + 6 + 9 x + 12 x - 20] = \frac{1}{2} [28 x - 14] = 14 x - 7$

since area of triangle DBC/area of triangle ABC=1/2

$\frac{14 x - 7}{49 / 2} = \frac{1}{2} 28 x - 14 = \frac{49}{2} 28 x = 14 + 24.5 28 x = 38.5 x = \frac{38.5}{28} = 1.375$

Four points A(6,3) , B(-3,5) , C(4,-2) , and D(x,3x) are given in such a way that area of triangle DBC/area of triangle ABC =1/2. Find x

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

area of triangle DBC/area of triangle ABC =1/2. Find x