Question

A (-1, 1), B (1, 3) and C (3, a) are points and if AB = BC, then find 'a'.​
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Answer 1

$\huge \red{\bf{solution}} \\ \\ given \: that \\ A \: ( - 1, \: 1) \:, \: \: B(1, \: 3) \: \:, \: C(3 ,\: a) \\ \\ A.T.Q \: \\ \implies \: AB = BC \: ........(1) \\ \\ firstly \: find \: distance \: of\: A \: B \\ \\AB \implies \: \sqrt{ {(1 +1)}^{2}+{(3-1)}^{2} } \\ \\ AB \implies \: \sqrt{ 8 } \\ \\ now \: find \: distance \: of \: BC \\ \\ BC \implies \: \sqrt{ {(3 - 1)}^{2} + {(a - 3)}^{2} } \\ \\ BC \implies \: \sqrt{4 + {(a - 3)}^{2} } \\ from \: equation \: (1) \\ \\ \implies \: AB = BC \\ \\ \implies \: \sqrt{8} = \sqrt{4 + {(a - 3)}^{2} } \\ taking \: square \: on \: both \: side \\ \\ \implies \: 8 = 4 + {a}^{2} + 9 - 6a \\ \\ \implies \: {a}^{2} - 6a + 5 \\ \\ here \: a \: has \: two \: values \: \\ \\ (a - 1)(a - 5) \\ \\\boxed{ a = 1 ,\: 5}\\ \\ here \:we\:used\: distance \: formula$

Answer 2

Step-by-step explanation:

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