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Determinants

Question

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Find values of k if area of triangle is 4 sq. units and vertices are (– 2, 0), (0, 4), (0, k)

Solution

Since area of triangle formed by the points (k, 0), (0, 4), (0, 2) is 4 sq. units.

therefore space space space 1 half space open vertical bar table row cell negative 2 end cell cell space space 0 end cell cell space space 1 end cell row 0 cell space space 4 end cell cell space space 1 end cell row 0 cell space space straight k end cell cell space space 1 end cell end table close vertical bar space equals space plus-or-minus space 4 space space space space space space rightwards double arrow space space space space space space space open vertical bar table row cell negative 2 end cell cell space space 0 end cell cell space space 1 end cell row 0 cell space space 4 end cell cell space space 1 end cell row 0 cell space space straight k end cell cell space space 1 end cell end table close vertical bar space equals space plus-or-minus space 8 therefore space space space space minus 2 open vertical bar table row 4 cell space space space 1 end cell row straight k cell space space space 1 end cell end table close vertical bar space equals space plus-or-minus 8 space space space space space space space space space space space space rightwards double arrow space space space space space space space minus 2 left parenthesis 4 minus straight k right parenthesis space equals space plus-or-minus 8 therefore space space space space space minus 8 plus 2 space straight k space equals space 8 comma space minus 8 space space space space space space space space space space space space rightwards double arrow space space space space space 2 space straight k space equals space 16 comma space 0 therefore space space space space space space space straight k space equals space 0 comma space space 8 space space

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