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Determinants

Question

Wired Faculty App

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

Solution

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

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

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