Question

The points of quadrilateral and are (6,3),(-3,5),(4,-2)(k,3k).if


ar(dbc)/ar(abc)=1/2,find the value of k

Answer 1

$\frac{area \: of \: dbc}{area \: of \: abc} = \frac{1}{2} \\ \frac{k(5 + 2) - 3( - 2 - 3k) + 4(3k - 5)}{6(5 + 2) - 3( - 2 - 3) + 4(3 - 5)} = \frac{1}{2} \\ \frac{7k + 6 + 9k + 12k - 20}{42 + 15 - 8} = \frac{1}{2} \\ \frac{28k - 14}{49} = \frac{1}{2} \\ 56k - 28 = 49 \\ 56k = 77 \\ k = \frac{77}{56} = \frac{11}{8}$