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Question

If A=(-3,4),B=(-1,-2),C=(5,6),D(x,-4)are vertices of a quadrilateral such thatar(ABD)=2ar(ACD) then x is equal to


A

6

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B

9

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C

69

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D

96

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Solution

The correct option is C

69


The explanation for the correct option:

Step 1. Writing the given data:

Given,

A=(-3,4),B=(-1,-2),C=(5,6),D(x,-4)

and, ABD=2ACD

Step 2. Find the value of x:

Area (ABD)=12|(-3)(-2+4)+(-1)(-4-4)+x(4-(-2)| [Area()=(12)|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|]

=12|2+6x|=|1+3x|

Similarly,

Area (ACD)=12|(-3)(6+4)+5(-4-4)+x(4-6)|

=12|70+2x|

ABD=2ACD

1+3x=212(70+2x)

1+3x=70+2x

x=69

Hence, the correct option is (C)


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