Find the area of the triangle whose vertices are ( - 8, 4), ( - 6, 6) and ( - 3, 9).

Given,

Let the vertices of triangle;

(x_{1}, y_{1}) → ( - 8, 4)

(x_{2}, y_{2}) = ( - 6, 6)

(x_{3}, y_{3}) = ( - 3, 9)

We know that, the area of triangle with vertices (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3})

Area of triangle = 1/2 [x_{1} (y_{2} - y_{3} ) + x_{2} (y_{3} - y_{1} ) + x_{3} (y_{1} - y_{2} )]=0

= 1/2 [ - 8(6 – 9) – 6(9 – 4) + ( - 3)(4 – 6)]

= 1/2 [ - 8( - 3) – 6(5) – 3( - 2)]

= 1/2 24 – 30 + 6)

= 1/2 (30 – 30)

= 1/2 (0) = 0

Hence, the area of triangle is 0.

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