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Determinants

Question
CBSEENMA12034485

Find the area of the triangle with vertices at the points given in each of the following:
(1, 0)  (6,0), (4, 3) 

Solution
Let ∆ be the area of the triangle whose vertices are (1,0), (6, 0), (4,3).
therefore space space space space space space space increment space equals space 1 half open vertical bar table row 1 cell space space 0 end cell cell space space 1 end cell row 6 cell space 0 end cell cell space space 1 end cell row 4 cell space 3 end cell cell space space 1 end cell end table close vertical bar space equals space 1 half open square brackets 1 space open vertical bar table row 0 cell space space space 1 end cell row 3 cell space space space space 1 end cell end table close vertical bar plus 1 space open vertical bar table row 6 cell space space space 0 end cell row 4 cell space space space space 3 end cell end table close vertical bar close square brackets
space space space space space space space space space space space space space space space space equals space 1 half open square brackets 1 left parenthesis 0 minus 3 right parenthesis plus 1 space left parenthesis 18 minus 0 right parenthesis close square brackets space equals space 1 half left parenthesis negative 3 plus 18 right parenthesis space equals space 15 over 2 space equals space 7.5 space sq. space units.

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