Question

Find the area of a triangle whose vertices are given as (1, - 1) (-4, 6) and ir
(-3,-5).

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Answer 1

Answer:

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Answer 2

$\tt Area\:of\:triangle\:whose\:vertices\:are\:({x}_{1},{y}_{1}), \\ \tt ({x}_{2},{y}_{2}) \:and\:({x}_{3},{y}_{3})\:is\:given\:by \\ \\ \tt \boxed{\bold{\underline{\green{\tt A = \frac{1}{2} \left[ \tt \begin{array}{ c c c } \tt {x}_{1}& \tt {y}_{1}& \tt 1 \\ \tt {x}_{2} & \tt {y}_{2} & \tt 1 \\ \tt {x}_{3} & \tt {y}_{3} & \tt 1 \end{array} \right ] }}}} \\ \\ \tt Area\:of\:triangle\:whose\:vertices\:are\:(1,-1) \\ \tt (-4,6) \:and\:(-3,-5) \:is\:given\:by \\ \\ \tt A = \frac{1}{2} \left[ \begin{array}{ c c c } 1 &-1&1 \\ -4 & 6 & 1 \\ -3 & -5 & 1 \end{array} \right ] \\ \\ \tt = \frac{1}{2}( 1(6+5) + 1(-4+3) +1(20+18) ) \\ \\ \tt = \frac{1}{2}(11 - 1 + 38 ) \\ \\ \frac{1}{2} × 48 \\ \\ \tt = 24 \: sq.units \\ \\ \tt \boxed{\bold{\underline{\red{\tt A = 24 \:sq.units }}}}$