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 answer:

x =  2
y =  -1

Step-by-step explanation:

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=102204​=2  x=2
y=(5⋅ x−16)/6=(5⋅ 2−16)/6=−1

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