Question

consider the points A(1,0),B(4,0) and C(1,4).then the triangle ABC is a​

Answer 1

The triangle ABC formed A(1,0),B(4,0) and C(1,4) will be a right angled triangle.

Distance formula :

$\sqrt{ (x _2 - x_1) ^{2} +(y_2 - y_1) ^{2} }$

Length of AB

$= \sqrt{ ({4 - 1}^{2}) + {0}^{2} } \\ = \sqrt{ {3}^{2} } \\ = 3cm$

Length of BC

$= \sqrt{ {(1 - 4)}^{2} + ( {4 - 0}^{2}) } \\ = \sqrt{ {3}^{2} + {4}^{2} } \\ = \sqrt{25} \\ = 5cm$

Length of AC

$= \sqrt{ ({1 - 1})^{2} + {4}^{2} } \\ = \sqrt{ {4}^{2} } \\ = 4cm$

We observe that,

BC² = AB² + AC²

5² = 3² + 4²

25 = 25

Therefore, Triangle formed is Right angled triangle, right angled at A