find the area of a triangle ABC whose vertices are A(1,-1) B(-4,6) and (-3,-5)

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Question

find the area of a triangle ABC whose vertices are A(1,-1)
B(-4,6) and (-3,-5)

Vimala · Accepted Answer

The area of a triangle, the coordinates of whose vertices are $A (x_{1}, y_{1}), B (x_{2}, y_{2}), C (x_{3}, y_{3})$ is

$A r e a = \frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |$

Let $A = (x_{1}, y_{1}) = (1, - 1), B = (x_{2}, y_{2}) = (- 4, 6), C = (x_{3}, y_{3}) = (- 3, - 5)$ be the given points.

Then,

$A r e a o f Δ A B C = \frac{1}{2} | 1 (6 + 5) - 4 (- 5 + 1) - 3 (- 1 - 6) | = \frac{1}{2} | 11 + 16 + 21 | = \frac{1}{2} | 48 | = 24 s q . u n i t s$