Write the formula for area of triangle $A B C$ where A $(x_{1}, y_{1}), B (x_{2}, y_{2})$ and $C (x_{3}, y_{3})$

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Solution

$A (x_{1}, y_{1}) B (x_{2}, y_{2}) C (x_{3}, y_{3})$

Area of $Δ = \frac{1}{2} x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + (y_{1} - y_{2})$

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(x_{1}, y_{1}), B (x_{x}, y_{2})

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Find the centroid of the triangle with vertices A $(x_{1}, y_{1})$ , B $(x_{2}, y_{2})$ and C $(x_{3}, y_{3})$ .

A (x_{1}, y_{1}), B (x_{2}, y_{2}), C (x_{3}, y_{3})

(x_{1} - 4)^{2} + (y_{1} - 5)^{2} = (x_{2} - 4)^{2} + (y_{2} - 5)^{2} = (x_{3} - 4)^{2} + (y_{3} - 5)^{2},

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The area of triangle with vertices $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ is:

Find the centroid of the triangle with vertices A $(x_{1}, y_{1})$ , B $(x_{2}, y_{2})$ and C $(x_{3}, y_{3})$ .

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