Question

3) prove that by joining (2, 1), (3, 4), (- 3, 6) we get a hight triangle​

Answer 1

Answer:

${ab}^{2} + {bc}^{2} = {ca}^{2} .$

THEREFORE ABC IS A RIGHT ANGLE TRIANGLE.

Step-by-step explanation:

$a(2 \: \: \: \: \: \: 1) \: \: \: \: \: \: \: b(3 \: \: \: \: \: 4) \: \: \: \: \: \: c( - 3 \: \: \: \: \: \: \: 6) \\ \\ \\ {ab}^{} = \sqrt{ {(2 - 3)}^{2} + {(1 - 4)}^{2} } \\ \\ = \sqrt{1 + 9} = \sqrt{10} \\ \\ \\ \\ bc = \sqrt{ {(3 + 3)}^{2} + {(4 - 6)}^{2} } \\ \\ = \sqrt{36 + 4} \\ \\ = \sqrt{40} \\ \\ = 2\sqrt{10} \\ \\ ca = \sqrt{ {(2 + 3)}^{2} + {(1 - 6)}^{2} } \\ \\ = \sqrt{25 + 25} \\ \\ = 5 \sqrt{2} \\ \\ \\ \\ as \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {ab}^{2} + {bc}^{2} = {ca}^{2} .$