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x + 3y + 2 = 0 ---> x = -3y -2
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(-3y -2)² - 6*(-3y -2) + y² -2y + 2 = 0
9y² +12y + 4 +18y +12 + y² - 2y + 2 = 0
10 y² + 28 y + 18 = 0
5 y² + 14 y + 9 = 0
Δ = 14² -4*5*9 = 196 - 180 = 16
√Δ = 4
y1 = [-14 - 4]/10 = -18 /10 = -1,8
y2 = [-14 + 4]/10 = -10/ 10 = -1,0
x1 = -3*(-1,8) -2 = 3,4
x2 = -3*(-1 ) - 2 = 3 - 2 = 1
A = ( 1; -1) , B = ( 3,4 ; -1,8)
-->
AB = [3,4 - 1; -1,8 -(-1)] = [2,4 ; -0,8 ]
I AB I² = (2,4)² + (-0,8)² = 5,76 + 0,64 = 6,4
I AB I = √6,4