The coordinates of A,B,   C  and D   are 6,3 ,   (−3,5),   4,−2  and (x,3x)   respectively. If ar(ΔDBC):ar(ΔABC)=1:2,   then the value of x   from the following choices is:

# The coordinates of    and   are      and   respectively. If   then the value of   from the following choices is:

1. A
1.25
2. B
2
3. C
1.375
4. D
2.25

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### Solution:

It is given that the coordinates are A(6, 3), B(-3, 5), C(4, -2), D(x, 3x).
We first find the area of the triangles   and then find the ratio to equate it to the given ratio  .
The area of the triangle with the coordinates   is given by the formula,

Calculation of area of  .
Here,

The area of the   is given by,
Calculation of area of  .

The area of the   is,

Hence,

The value of   is  .
Hence, option 3) is correct.

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