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:

x_{0} = - 3; y_{0} = 4 x_{1} = 1; y_{1} = 6 (x - x_{0})^{2} + (y - y_{0})^{2} = (x - x_{1})^{2} + (y - y_{1})^{2} 5 \cdot x - 6 \cdot y - 16 = 0 y = (5 \cdot x - 16) / 6 (x - x_{0})^{2} + ((5 \cdot x - 16) / 6 - y_{0})^{2} = (x - x_{1})^{2} + ((5 \cdot x - 16) / 6 - y_{1})^{2} (x + 3)^{2} + ((5 \cdot x - 16) / 6 - 4)^{2} = (x - 1)^{2} + ((5 \cdot x - 16) / 6 - 6)^{2} x^{2} + 6 x + 9 + 25 / 36 x^{2} - 100 x / 9 + 400 / 9 = x^{2} - 2 x + 1 + 25 / 36 x^{2} - 130 x / 9 + 676 / 9 6 \cdot x + 9 - 100 \cdot x / 9 + 400 / 9 = - 2 \cdot x + 1 - 130 \cdot x / 9 + 676 / 9 102 x = 204 x = 2

y = (5 \cdot x - 16) / 6 = (5 \cdot 2 - 16) / 6 = - 1

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