On a line

On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].

Correct result:

x =  9
y =  6

Solution:

3x−4y−3=0  x=(3+4y)/3=9 y=(3x−3)/4 ∣AC∣=∣BC∣  (x−4)2+(y−4)2=(x−7)2+(y−1)2  (x−4)2+((3x−3)/4−4)2=(x−7)2+((3x−3)/4−1)2 1.5x=13.5 32x=272 3x=27 x=27/3=9 
y=(3x−3)/4=(3⋅ 9−3)/4=6

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