Çözüldü Coordinate Geometry

What is the difference of the ordinates for the points A and B on the line y = 3x - 1 of which the length in between is 3√10 units?
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The vertices of the right triangle ACB are located at;
A(a, 3a - 1)
B(b, 3b - 1)
C(b, 3a - 1)
sin(∡BAC) = sin[ arctan(3) ] = 3 / √(3^2 + 1^2) = 3 / √10....(I)
sin(∡BAC) = [ 3b - 1 - (3a - 1) ] / (3√10) = 3(b - a) / (3√10) = (b - a) / √10....(II)
From the equations (I) and (II), b - a = 3....(III)
Difference of the ordinates; 3b - 1 - (3a - 1) = 3(b - a)....(IV)
Substituting the value (III) in (IV); 3·3 = 9 units