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  (xx0)2+(yy0)2=(xx1)2+(yy1)2 5 x6 y16=0  y=(5 x16)/6  (xx0)2+((5 x16)/6y0)2=(xx1)2+((5 x16)/6y1)2 (x+3)2+((5 x16)/64)2=(x1)2+((5 x16)/66)2 x2+6x+9+25/36x2100x/9+400/9=x22x+1+25/36x2130x/9+676/9   6 x+9100 x/9+400/9=2 x+1130 x/9+676/9  102x=204  x=2
y=(5 x16)/6=(5 216)/6=1



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For Basic calculations in analytic geometry is a helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
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Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
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