Mathematics

Mathematics

Problem

For vertices (x1,y1)(x_1,y_1), (x2,y2)(x_2,y_2) and (x3,y3)(x_3,y_3), which of the following formulas represents the area AA of the triangle they form? a) ∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)| b) 12(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))\dfrac12\bigl(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\bigr) c) 12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣\dfrac12\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right| d) 12∣x1(y2+y3)+x2(y3+y1)+x3(y1+y2)∣\dfrac12\left|x_1(y_2+y_3)+x_2(y_3+y_1)+x_3(y_1+y_2)\right|

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