Question

If the points A(m,n),B(7,3)andC(-3,-5)are such that AB=AC,then

Answer 1

$ab = ac$
${(ab)}^{2} = {(ac)}^{2}$
${(m - 7)}^{2} + {(n - 3)}^{2} = {(m + 3)}^{2} + {(n + 5)}^{2}$
${m}^{2} + 49 - 14m + {n}^{2} + 9 - 6n = {m}^{2} + 9 + 6m + {n}^{2} + 25 + 10n$
$49 - 14m + 9 - 6n - 9 - 6m - 25 - 10n = 0$
$24 - 20m - 16n= 0$
$6 - 5m - 4n = 0$
$5m + 4n - 6 = 0$