Q82 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Mathematics

The triangle with vertices at $(-2,2),(2,-2)$ and $(1,1)$ is

  • A
    scalene triangle
  • B
    equilateral triangle
  • Correct answer
    C
    isosceles triangle
  • D
    right-angled triangle

Solution

Let $A(-2,2), B(2,-2)$ and $C(1,1)$ are the vertices of $\triangle A B C$. $$ \begin{array}{r} A B=\sqrt{(2+2)^2+(-2-2)^2}=\sqrt{4+4}=4 \sqrt{2} \\ B C=\sqrt{(1-2)^2+(1+2)^2}=\sqrt{1+9}=\sqrt{10} \\ A C=\sqrt{(1+2)^2+(1-2)^2}=\sqrt{9+1}=\sqrt{10} \end{array} $$ $\triangle A B C$ is an isosceles triangle.

Hence, the correct answer is option: 'C'.

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