Question

find k is distance between A(k,-8) and B(-7,-3) is 13​

Answer 1

Answer:

$by \: distance \: formula$

$ab = \sqrt{ {( - 7 - k)}^{2} + ( { - 3 + 8)}^{2} } = 13$

$ab = \sqrt{ {( - 7 - k)}^{2} + 25 } = 13$

$ab = ( { - 7 - k)}^{2} + 25 = 169$

$ab = 49 + {k}^{2} + 14k + 25 = 169$

$= {k}^{2} + 14k + 74 = 169$

$= {k}^{2} + 14k = 169 - 74$

${k}^{2} + 14k = 95$

${k}^{2} + 19k - 5k - 95 = 0$

$k(k + 19) - 5(k + 19) = 0$

$(k - 5)(k + 19) = 0$

$k = 5 \: and \: k = - 19$

the required answer is k=5

hence proved it