Question

Given A = ( 3 , 1 ) and B = ( 0, y - 1 ) find y if AB = 5​

Answer 1

$AB = 5$

$AB {}^{2} = 5$

$(0 - 3) {}^{2} + (y \: - 1 - 1) {}^{2} = 25$

$9 + \: y {}^{2} + 4 \: - 4y = 25$

$y {}^{2} - 4y - 12 = 0$

$y(y - 6) + 2(y - 6) = 0$

$(y - 6)(y + 2) = 0$

$y = 6 , -2$