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

  • question_answer
    If two vertices of a triangle are (6,4), (2,6) and its centroid is (4, 6), then the third vertex is   [RPET 1996]

    A) (4, 8)

    B) (8, 4)

    C) (6, 4)

    D) None of these

    Correct Answer: A

    Solution :

    \[x=\frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\,\,y=\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3}\] \[\therefore \,\,4=\frac{6+2+{{x}_{3}}}{3},\,\,6=\frac{4+6+{{y}_{3}}}{3}\]\[\Rightarrow \,\,\,{{x}_{3}}=4,\,\,{{y}_{3}}=8\] \[\therefore \] Third vertex is (4, 8).


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