If the distance between the points A(2,1) and B(8,y) is 10 units find the value of y.. Created by subedisadikshya76. Math

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If the distance between the points A(2,1) and B(8,y) is 10 units find the value ...

ANSWER :-

$10 = \sqrt{ {(8 - 2)}^{2} + {(y - 1)}^{2} } \\ \implies \: {10 }^{2} = {6}^{2} + {(y - 1)}^{2} \\ 100 = 36 + {y}^{2} + 1 - 2y \\ 100 - 37 = {y}^{2} - 2y \\ {y}^{2} - 2y - 63 = 0 \\ {y}^{2} - 9y + 7y - 63 = 0 \\ y(y - 9) + 7(y - 9) = 0 \\ \implies(y - 9) = 0 \: or \: (y + 7) = 0 \\ y = 9 \: or - 7$

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