Question

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

Answer 1

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

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

Using distance formula,

d = √ ((x2– x1)²+ (y2– y1)²)

AB = √((-4+5)² + (-2-6)²)

= √(1+64)

=√65

BC=√((7+4)² + (5+2)²)

=√(121 + 49)

=√170

AC=√((7+5)² + (5-6)²)

=√144 + 1

=√145

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

Answer 2

Given ,

The triangle ABC whose vertices are A(-5,6) , B(-4,-2) and C(7,5)

We know that , the distance formula is given by

$\large \sf \fbox{D = \sqrt{ {( x_{2} - x_{1} ) }^{2} + { (y_{2} - y_{1} )}^{2} } \: \: }$

Thus , the distance between A(-5,6) , B(-4,-2) will be

$\sf \mapsto AB = \sqrt{ {( - 4 + 5)}^{2} + {( - 2 - 6)}^{2} } \\ \\ \sf \mapsto AB = \sqrt{1 + 64} \\ \\ \sf \mapsto AB = \sqrt{65} \: \: units$

Similarly , the distance between B(-4,-2) , C(7,5) and A(-5,6) , C(7,5) will be

$\sf \mapsto BC = \sqrt{170} \: \: units\\ \\ \sf \mapsto AC = \sqrt{145} \: \: units$

Since , AB ≠ BC ≠ AC

$\therefore \sf \underline{The \: triangle \: ABC \: is \: scalene \: triangle }$