Question

Check whether A(5, − 1), B(6, 2) and C(7, −3) are the vertices of an isosceles triangle or not

Answer 1

$\textbf{Given:}$

$\textsf{Points are A(5,-1), B(6,2), C(7,-3)}$

$\textbf{To find:}$

$\textsf{whether ABC is a isoceles triagnle or not}$

$\textbf{Solution:}$

$\mathsf{AB=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}}$

$\mathsf{AB=\sqrt{(5-6)^2+(-1-2)^2}}$

$\mathsf{AB=\sqrt{(-1)^2+(-3)^2}}$

$\mathsf{AB=\sqrt{1+9}}$

$\implies\boxed{\mathsf{AB=\sqrt{10}}}$

$\mathsf{BC=\sqrt{(6-7)^2+(2+3)^2}}$

$\mathsf{BC=\sqrt{1^2+5^2}}$

$\mathsf{BC=\sqrt{1+25}}$

$\implies\boxed{\mathsf{BC=\sqrt{26}}}$

$\mathsf{AC=\sqrt{(5-7)^2+(-1+3)^2}}$

$\mathsf{AC=\sqrt{(-2)^2+2^2}}$

$\mathsf{AC=\sqrt{4+4}}$

$\implies\boxed{\mathsf{AC=\sqrt{8}}}$

$\textsf{It is clear that, the lengths of no two sides are equal}$

$\textsf{Hence, ABC is not an isoceles triangle}$

Find more:

Prove that the vertices of A(-2,3) B(4,3) C(4,-1) and D(-2,-1) form a Rectangle ​

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