Given:
(x1,y1) = (0,0)
(x2,y2) = (0,-10)
Using the angle to C, how are the coordinates at C calculated?

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Let A be the point (x1,y1) and B be the point (x2,y2).
AC must have length 10 since it is isosceles.
Let X the point on AB which a perpendicular line passes through C. AXC is a right angled triangle with hypotenuse AC. C has co-ordinates
(-length(AX),length(XC)).Therefore C has co-ordinates:
(-10*cos(theta),10*sin(theta))