Do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.

Open in App

Solution

Let the given points be,

$\Rightarrow A (3, 2), B (- 2, - 3)$ and $C (2, 3)$

Therefore,

$A B = \sqrt{{(3 + 2)}^{2} + {(2 + 3)}^{2}} = \sqrt{50} = 5 \sqrt{2} u n i t s$

$B C = \sqrt{{(- 2 - 2)}^{2} + {(- 3 - 3)}^{2}} = \sqrt{52} = 2 \sqrt{13} u n i t s$

$A C = \sqrt{{(3 - 2)}^{2} + {(2 - 3)}^{2}} = \sqrt{2} u n i t s$

Now, we can see that,

${(2 \sqrt{13})}^{2} = {(5 \sqrt{2})}^{2} + {(\sqrt{2})}^{2}$

$B C^{2} = A B^{2} + A C^{2}$

Therefore, the given triangle is a right angled triangle.

Suggest Corrections

Similar questions

Prove that the points (2, 3), (-4, -6) and $(1, \frac{3}{2})$ do not form a triangle.

z_{1}, z_{2}

z_{3}

\frac{z_{1} - z_{3}}{z_{2} - z_{3}} = \frac{1 - i \sqrt{3}}{2}

z_{1}, z_{2}

z_{3}

P Q R

P (- \sqrt{2}, \sqrt{2}), Q (- \sqrt{2}, - \sqrt{2})

R (- \sqrt{6}, \sqrt{6})

Name the type of triangle formed by the points A(-5,6), B(-4,-2) and C(7,5).

Join BYJU'S Learning Program