Question

find the distance between A (9,a) and B(a,2) is 5unit​

Answer 1

Answer:

$a = 5 \: \: \: \: \: \: a = 6.$

Step-by-step explanation:

$(9 \: \: \: \: \: a) \: \: \: ( a \: \: \: \: \: \: \: \: 2) \\ \\ \sqrt{ {(a - 9)}^{2} + {(a - 2)}^{2} } = 5 \\ \\ {(a - 9)}^{2} + {(a - 2)}^{2} = 25 \\ \\ {a}^{2} + 81 - 18a + {a}^{2} + 4 - 4a = 25 \\ \\ 2 {a}^{2} - 22a + 85 = 25 \\ \\ 2 {a}^{2} - 22a - 60 = 0 \\ \\ {a}^{2} - 11a - 3 0 = 0 \\ \\ {a}^{2} - 6a - 5a - 30 = 0 \\ \\ a(a - 6) - 5(a - 6) = 0 \\ \\ (a - 5)(a - 6) = 0 \\ \\ a = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: a = 6.$