Find the coordinates in an isosceles triangle

Question

Given:

(x1,y1) = (0,0)

(x2,y2) = (0,-10)

Using the angle to C, how are the coordinates at C calculated?

Answer 1

There are multiple valid answers to this question. The following coordinates all produce isosceles triangles:

(-10, 0)
(10, 0)
(-10, -10)
(10, -10)
(6, -8)
(-6, -8)
(8, -6)
(-8, -6)
(x, -5) | x != 0

And, as a matter of fact, this isn't a complete solution.

Without some hint as to what programming platform you intend to implement a solution in, we cannot help much more.

Answer 2

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)).

length(AX) = length(AC)*cos(theta) = 10*cos(theta)

length(XC) = length(AC)*sin(theta) = 10*sin(theta)

Therefore C has co-ordinates: (-10*cos(theta),10*sin(theta))