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Determinants

Question

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Find the area of the triangle, whose vertices are (3, 1), (4, 3) and (-5, 4).

Solution

Let ∆ be the area of the triangle whose vertices are (3, 1), (4, 3), (–5, 4).

therefore space space space space increment space equals space 1 half open vertical bar table row 3 cell space space 1 end cell cell space space 1 end cell row 4 cell space 3 end cell cell space space 1 end cell row cell negative 5 end cell cell space 1 end cell cell space space 1 end cell end table close vertical bar space equals space 1 half open vertical bar table row 3 cell space 1 end cell cell space 1 end cell row 1 cell space 2 end cell cell space 0 end cell row cell negative 8 end cell cell space 3 end cell cell space 0 end cell end table close vertical bar comma space by space straight R subscript 2 minus straight R subscript 1 comma space space straight R subscript 3 minus straight R subscript 1 space space space space space space space space space space space space space space equals space 1 half open vertical bar table row 1 cell space space space 2 end cell row cell negative 8 end cell cell space space space 3 end cell end table close vertical bar space equals space 1 half left parenthesis 3 plus 16 right parenthesis space equals space 19 over 2 sq. space units. space

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