Question

the length of line segment is 10 units. if one end point is (2,-3) & abcissa of second end point is 10 show that it's ordinates are 3 or -9

Answer 1

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Answer 2

$let \: ordinate \: of \: second \: be \: y \\ 10 = \sqrt{ {(2 - 10)}^{2} + {( - 3 - y)}^{2} } \\ 100 = {( - 8)}^{2} + {( - 3 - y)}^{2} \\ 100 = 64 + 9 + {y}^{2} + 6y \\ {y}^{2} + 6y - 27 = 0 \\ {y }^{2} + 9y - 3y - 27 = 0 \\ y(y + 9) - 3(y + 9) = 0 \\ (y + 9)(y - 3) = 0 \\ y = - 9 \: \: or \: \: y = 3$