Given the points a (5, y), B (1,2), and the vector AB = 5, then y=

AB=(1-5,2-y)=(-4,2-y)
also
Vector AB = 5,
Namely
√(-4)²＋(2-y)²=5
16+4-4y+y²=25
y²-4y-5=0
(y+1)(y-5)=0
Y = - 1 or y = 5

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