Question

A(-8;6) B(12;2) C(4;-6) prove that triangle ABC is a right angled triangle

Answer 1

Explanation:

$Given \: points \: \\ A( - 8 \:, 6) \:, B(12 \:, 2) \:, C(4 \:, - 6) \\ AB = \sqrt{ { (- 8 - 12)}^{2} + {(6 - 2)}^{2} } \\ AB = \sqrt{400 + 16} = \sqrt{416} \\ \\ BC = \sqrt{ {(12 - 4)}^{2} + {(2 + 6)}^{2} } \\ BC = \sqrt{64 + 64} = \sqrt{128} \\ \\ AC = \sqrt{( { - 8 - 4)}^{2} + ( {6 + 6)}^{2} } \\ AC = \sqrt{144 + 144} = \sqrt{288} \\ We \: observe \: that \\ {(AB)}^{2} = ( {BC)}^{2} + ( {AC)}^{2} \\ then \:, \: these \: points \: form \: a \: right \: angled \: \\ triangle. \\ \\ \\ hope \: it \: will \: help \: you.$