JEE Main & Advanced AIEEE Solved Paper-2002

  • question_answer
    A triangle with vertices (4, 0), (-1, -1), (3, 5) is

    A) isosceles and right angled

    B) isosceles but not right angled

    C) right angled but not isosceles

    D) neither right angled nor isosceles

    Correct Answer: A

    Solution :

    (i) A triangle is isosceles, if its any two sides are equal, so to prove a triangle isosceles, we have to prove as two sides are equal. (ii) To prove a triangle a right angled triangle, we have to prove that the sum of square of any two sides is equal to the square of third side. Let points A (4, 0), B (-1, - 1) and C(3, 5) be the vertices of a \[\Delta ABC\]. \[\therefore AB=\sqrt{(-1-{{4}^{2}}+{{(-1-0)}^{2}}}=\sqrt{25+1}=\sqrt{26}\]    \[BC=\sqrt{{{(3+1)}^{2}}+{{(5+1)}^{2}}}\]    \[=\sqrt{{{4}^{2}}+{{6}^{2}}}\]    \[=\sqrt{16+36}=\sqrt{52}\] and \[CA=\sqrt{{{(4-3)}^{2}}+{{(0-5)}^{2}}}=\sqrt{1+25}=\sqrt{26}\] Now, \[C{{A}^{2}}+A{{B}^{2}}={{(\sqrt{26})}^{2}}+{{(\sqrt{26})}^{2}}\]                                    \[=26+26=52=B{{C}^{2}}\] \[\Rightarrow \]   \[C{{A}^{2}}+A{{B}^{2}}=B{{C}^{2}}\] Thus, the triangle is isosceles and right angled triangle.

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