2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Rectangular Cartesian Coordinates

JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank Points related to triangle (Orthocente Circumcentre Incentre), Area of some geometrical figures Collinearity

  • question_answer
    The area of the triangle with vertices at \[(-4,\text{ }1),\,(1,\text{ }2),\,(4,\text{ }-3)\] is      [EAMCET 1980]

    A) 14

    B) 16

    C) 15

    D) None of these

    Correct Answer: A

    Solution :

    Area of triangle \[=\frac{1}{2}\,\left| \,\begin{matrix}    {{x}_{1}} & {{y}_{1}} & 1  \\    {{x}_{2}} & {{y}_{2}} & 1  \\    {{x}_{3}} & {{y}_{3}} & 1  \\ \end{matrix}\, \right|\]\[=\frac{1}{2}\,\left| \,\begin{matrix}    -4 & 1 & 1  \\    1 & 2 & 1  \\    4 & -3 & 1  \\ \end{matrix}\, \right|\,\]              = \[\frac{1}{2}[-4\,(2+3)-1\,(1-4)+1\,(-3-8)\]             \[=\frac{1}{2}\,|\,-28|=14\] units.


You need to login to perform this action.
You will be redirected in 3 sec spinner