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If B is the midpoint of AC, then |AB| = |AC|.
|AB| = 3x + 2
|BC| = 5x - 10
Therefore we have the equation:
3x + 2 = 5x - 10 |subtract 2 from both sides
3x = 5x - 12 |subtract 5x from both sides
-2x = -12 |divide both sides by (-2)
x = 6
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0.1 repeating as a fraction is 1/9
Y = -3x + 6
y - 6 = -3x
-1/3 y + 2 = x
z = x -3
z = -1/3 y + 2 -3 = -1/3 y - 1
set z = 0
-1/3 y = 1
y = -3
set y = 0
z = - 1