The points $(5,-4,5),(-3,-3,2)$ and $(-1,-6,8)$ form ......

The points $(5,-4,5),(-3,-3,2)$ and $(-1,-6,8)$ form ......
  1. an isosceles triangle
  2. an equilateral triangle
  3. a right-angled isosceles triangle
  4. a right-angled triangle

Solution

Given points $A(5,-4,5), B(-3,-3,2)$ and $ \begin{aligned} & C(-1,-6,8) \\ & \therefore \quad A B=\sqrt{64+1+9}=\sqrt{74} \\ & B C=\sqrt{4+9+36}=7 \\ & \text { and } \quad C A=\sqrt{36+4+9}=7 \end{aligned} $ $\because$ Length of sides $B C$ and $C A$ are equal, but $B C^2+C A^2 \neq A B^2$ $\therefore \triangle A B C$ is an isosceles triangle

Asked in: AP EAMCET 2020 (22 Sep Shift 1)

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