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Question: If A(6, 3 ), B(–3, 5), C (4, –2) and D(x, 3x) are four points. If the ratio of area of DDBC and DABC...

If A(6, 3 ), B(–3, 5), C (4, –2) and D(x, 3x) are four points. If the ratio of area of DDBC and DABC is 1 : 2, then the value of x, will be-

A

118\frac{11}{8}

B

811\frac{8}{11}

C

3

D

None of these

Answer

118\frac{11}{8}

Explanation

Solution

AreaofΔDBCAreaofΔABC\frac{Areaof\Delta DBC}{Areaof\Delta ABC} = 12\frac{1}{2}

= 12[x(5+2)−3(−2−3x)+4(3x−5)]12[6(5+2)−3(−2+3)+4(3−5)]\frac{\frac{1}{2}\lbrack x(5 + 2) - 3( - 2 - 3x) + 4(3x - 5)\rbrack}{\frac{1}{2}\lbrack 6(5 + 2) - 3( - 2 + 3) + 4(3 - 5)\rbrack} = 12\frac{1}{2}

Ž 7x+6+9x+12x−207x−3−8\frac{7x + 6 + 9x + 12x - 20}{7x - 3 - 8} = 12\frac{1}{2}

Ž x = 118\frac{11}{8}