Question

the three point (- 2, 2), (8,- 2) and (- 4 - 3) are the vertices of: (1) an isosceles triangle, (2) an equilateral triangle, (3) a right angled triangle, (4) none of these​

Answer 1

Solution

let the vertices are A(- 2, 2), B(8,- 2) and C(- 4 - 3)

now..

$ab = \sqrt{( - 2 - 8) {}^{2} + (2 + 2) {}^{2} } \\ \: \: \: \: \: = \sqrt{100 + 16} = \sqrt{116} \\ bc = \sqrt{(8 + 4) {}^{2} + ( - 2 + 3) {}^{2} } \\ \: \: \: \: \: = \sqrt{144 + 1} = \sqrt{145} \\ ca = \sqrt{( - 4 + 2) {}^{2} +( - 3 - 2) {}^{2} } \\ \: \: \: \: \: = \sqrt{4 + 25} = \sqrt{29} \\ \\ now.... \\ ab {}^{2} + ca {}^{2} = ( \sqrt{116}) {}^{2} + ( \sqrt{29} ) {}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 116 + 29 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 145 = ( \sqrt{145} ) {}^{2} \\ = > ab {}^{2} + ca {}^{2} = bc {}^{2} \\ \\ therefore \: this \: is \: a \: right \: angled \: triangle...$

Answer 2

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Answer in Attachment

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