Which one of the following expressions gives the area of the triangle with vertices at

MATHEMATICS · Single correct · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Which one of the following expressions gives the area of the triangle with vertices at (x1,y1)(x_1,y_1), (x2,y2)(x_2,y_2) and (x3,y3)(x_3,y_3)? (a) 12(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))\dfrac{1}{2}\big(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\big) (b) 12∣x1(y2−y3)−x2(y3−y1)+x3(y1−y2)∣\dfrac{1}{2}\left|x_1(y_2-y_3)-x_2(y_3-y_1)+x_3(y_1-y_2)\right| (c) 12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣\dfrac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right| (d) ∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|

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