Coordinate Geometry - Area of Rectilinear Figures
Coordinate Geometry - Area of Rectilinear Figures
IP 3
The diagram shows a triangle with vertices \(A_1(x_1, y_1)\), \(A_2(x_2, y_2)\) and \(A_3(x_3, y_3)\). Verify the shoelace formula by showing that
Area of triangle \(A_1 A_2 A_3 = \frac{1}{2} \begin{vmatrix} x_1 & x_2 & x_3 & x_1 \\ y_1 & y_2 & y_3 & y_1 \end{vmatrix}\)
\( \, = \frac{1}{2} |x_1 y_2 + x_2 y_3 + x_3 y_1 - x_2 y_1 - x_3 y_2 - x_1 y_3|.\)
Triangle in a Cartesian plane
Solution:
Solution locked
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Answer:\(A=\dfrac12\left|x_1y_2+x_2y_3+x_3y_1-x_2y_1-x_3y_2-x_1y_3\right|\) (shown).
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