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Question

The centroid of a triangle lies at the origin and the coordinates of its two vertices are -8,7 and 9,4. The area of the triangle is


A

956

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B

-2852

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C

1903

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D

285

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Solution

The correct option is B

-2852


Explanation for the correct option:

Finding the centroid:

Centroid of the triangle formed by vertices (x1,y1),(x2,y2),(x3,y3) is given by

x=x1+x2+x33 and y=y1+y2+y33

Here, the centeroid is 0,0 and two vertices are -8,7 and 9,4.

Substitute the values.

0=-8+9+x33x3=-1

and

0=7+4+y33y3=-11

So, the vertices for triangle are -8,7,-1,-11 and 9,4.

Area of triangle with three vertices is 12x1y11x2y21x3y31.

Area=12-871941-1-111=12-84+11-79+1+1-99+4=12-120-70-95=-2852

Therefore, the correct answer is option (B).


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