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

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

Solution:

A (–5, 6), B (–4, –2) and C (7, 5) are the given points.

Now, using the distance formula,

$d~=\text{ }\surd \text{ }({{({{x}_{2}}~\text{ }{{x}_{1}})}^{2}}~+\text{ }{{({{y}_{2}}~\text{ }{{y}_{1}})}^{2}})$

$AB\text{ }=\text{ }\surd \left( \left( -4+5 \right){}^\text{2}\text{ }+\text{ }\left( -2-6 \right){}^\text{2} \right)$

$=\text{ }\surd 1+64$

$=\surd 65$

$BC=\surd \left( \left( 7+4 \right){}^\text{2}\text{ }+\text{ }\left( 5+2 \right){}^\text{2} \right)$

$=\surd 121\text{ }+\text{ }49$

$=\surd 170$

$AC=\surd \left( \left( 7+5 \right){}^\text{2}\text{ }+\text{ }\left( 5-6 \right){}^\text{2} \right)$

$=\surd 144\text{ }+\text{ }1$

$=\surd 145$

ABC is a scalene triangle, since all sides are of different length.

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