Isosceles triangle

In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.

Correct result:

x =  2
y =  -1

Solution:

x0=−3;y0=4 x1=1;y1=6  (x−x0)2+(y−y0)2=(x−x1)2+(y−y1)2 5⋅ x−6⋅ y−16=0  y=(5⋅ x−16)/6  (x−x0)2+((5⋅ x−16)/6−y0)2=(x−x1)2+((5⋅ x−16)/6−y1)2 (x+3)2+((5⋅ x−16)/6−4)2=(x−1)2+((5⋅ x−16)/6−6)2 x2+6x+9+25/36x2−100x/9+400/9=x2−2x+1+25/36x2−130x/9+676/9   6⋅ x+9−100⋅ x/9+400/9=−2⋅ x+1−130⋅ x/9+676/9  102x=204  x=2
y=(5⋅ x−16)/6=(5⋅ 2−16)/6=−1

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