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

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 Multiple Choice QuestionsLong Answer Type

146. A triangle has its three sides equal to a, b and c. If the coordinates of its vertices are A(x1 y1), B(x2, y2) and C(x3 y3), show that
space open vertical bar table row cell straight x subscript 1 end cell cell space space straight y subscript 1 end cell cell space 2 end cell row cell straight x subscript 2 end cell cell space straight y subscript 2 end cell cell space 2 end cell row cell straight x subscript 3 end cell cell space straight y subscript 3 end cell cell space 2 end cell end table close vertical bar squared space equals space left parenthesis straight a plus straight b plus straight c right parenthesis thin space left parenthesis straight b plus straight c minus straight a right parenthesis thin space left parenthesis straight c plus straight a minus straight b right parenthesis thin space left parenthesis straight a plus straight b minus straight c right parenthesis.

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 Multiple Choice QuestionsMultiple Choice Questions

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147. 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


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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 Multiple Choice QuestionsShort Answer Type

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Find the minor of element 6 in the determinant increment space equals space open vertical bar table row 1 cell space 2 end cell cell space 3 end cell row 4 cell space 5 end cell cell space 6 end cell row 7 cell space 8 end cell cell space 9 end cell end table close vertical bar

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150.

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open vertical bar table row 1 cell space space minus 2 end cell row 4 cell space space space 3 end cell end table close vertical bar.

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