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Determinants

Question
CBSEENMA12034486
Wired Faculty App

Find the area of the triangle with vertices at the points given in each of the following:
(2, 7), (1, 1), (10, 8)

Solution
Let ∆ be the area of thee triangle whose vertices are (2, 7), (1, 1), (10, 8).
therefore space space space space increment space equals space 1 half open vertical bar table row 2 cell space space space space 7 end cell cell space space space space 1 end cell row 1 cell space space space 1 end cell cell space space space space 1 end cell row 10 cell space space space 8 end cell cell space space space space space 1 end cell end table close vertical bar space space space space space space space space space space space space space equals space 1 half open vertical bar table row 2 cell space space space space space space space 7 end cell cell space space space space space 1 end cell row cell negative 1 end cell cell space space space minus 6 end cell cell space space space space space 0 end cell row 8 cell space space space space space 1 end cell cell space space space space space 0 end cell end table close vertical bar comma space space by space straight R subscript 2 space rightwards arrow space straight R subscript 2 minus straight R subscript 1 comma space space straight R subscript 3 space rightwards arrow straight R subscript 3 space minus straight R subscript 1 space space space space space space space space space space space space space space equals 1 half cross times 1 space open vertical bar table row cell negative 1 end cell cell space space space space space minus 6 end cell row 8 cell space space space space space space space space space space 1 end cell end table close vertical bar comma space by space expanding space with space straight C subscript 3 space space space space space space space space space space space space space space equals space 1 half left parenthesis negative 1 plus 48 right parenthesis space equals space 47 over 2 space equals space 23.5 space sq. space units. space

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