Name the type of triangle formed by the points A (–5, 6), B (–4,

Name: Name the type of triangle formed by the points A (–5, 6), B (–4, –2) and C (7, 5).
Uploaded: Wed, 2021-02-03 16:01
Description: Name the type of triangle formed by the points A (–5, 6), B (–4, –2) and C (7, 5).

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

Answers (1)

Solution.
Given vertices are A(–5, 6), B(–4, –2), C(7, 5)
$Distance \, formula= \sqrt{\left ( x_{2}-x_{1} \right )^{2}+\left ( y_{2}-y_{1} \right )^{2}}$
$Distance \, of\, AB= \sqrt{\left ( -4-\left ( -5 \right ) \right )^{2}+\left ( -2-6 \right )^{2}}$
                                  $= \sqrt{\left ( 1 \right )^{2}+\left ( -8 \right )^{2}}$
                                   $= \sqrt{1+64}$
                                    $= \sqrt{65}$
$Distance \, of\, BC= \sqrt{\left ( 7-\left ( -4 \right ) \right )^{2}+\left ( 5-\left ( -2 \right ) \right )^{2}}$
                                     $= \sqrt{\left ( 11 \right )^{2}+\left ( 7 \right )^{2}}$
                                       $= \sqrt{121+49}$
                                        $= \sqrt{170}$
$Distance \, of\, AC= \sqrt{\left ( 7-\left ( -5 \right ) \right )^{2}+\left ( 5-6 \right )^{2}}$
                                    $= \sqrt{\left ( 12 \right )^{2}+\left ( -1 \right )^{2}}$
                                       $=\sqrt{144+1}$
   $=\sqrt{145}$
$AB\neq BC\neq AC$
Therefore, ABC is a scalene triangle.