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Determinants

Question
CBSEENMA12034505
Wired Faculty App

If area of triangle is 35 sq. units with vertices (2, – 6), (5, 4) and (k, 4). Then k is

  • 12

  • -2

  • -12, -2

  • 12, -2

Solution

D.

12, -2

Since area of triangle formed by the points (2, -6), (5, 4), (k, 4) is 35 sq. units.
therefore space space space space 1 half open vertical bar table row 2 cell space space minus 6 end cell cell space space 1 end cell row 5 cell space space space space 4 end cell cell space space 1 end cell row straight k cell space space space 4 end cell cell space space 1 end cell end table close vertical bar space equals space plus-or-minus 35 space space space space space space space space space space space space space space space space rightwards double arrow space space space space open vertical bar table row 2 cell space minus 6 end cell cell space space 1 end cell row 5 cell space 4 end cell cell space space 1 end cell row straight k cell space 4 end cell cell space space 1 end cell end table close vertical bar space equals plus-or-minus 70 therefore space space space space 2 open vertical bar table row 4 cell space space 1 end cell row 4 cell space space space 1 end cell end table close vertical bar minus left parenthesis negative 6 right parenthesis space open vertical bar table row 5 cell space space 1 end cell row straight k cell space space 1 end cell end table close vertical bar plus space open vertical bar table row 5 cell space space space 4 end cell row straight k cell space space space 4 end cell end table close vertical bar equals space plus-or-minus 70 therefore space space space space 2 left parenthesis 4 minus 4 right parenthesis plus 6 left parenthesis 5 minus straight k right parenthesis plus 1 left parenthesis 20 minus 4 straight k right parenthesis space equals space plus-or-minus 70 therefore space space space space space 0 plus 30 minus 6 straight k plus 20 minus 4 straight k space equals 70 comma space space minus 70 therefore space space space space space space space space space space space minus 10 straight k space equals space 20 comma space minus 120 therefore space space space space space space space space space space space space space space space space space space straight k space equals negative 2 comma space space 12 therefore space space space space space space space space left parenthesis straight D right parenthesis space is space correct space answer

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