How do I calculate a triangle coordinate?

[RiaanSwiegers]

1. Calculate the coordinate of a triangle's 3rd corner when 2 corner coordinates and area is given (in Surveying).
Given:
Area of triangle ABC = 14994sqm
Corner B coordinate = +3541.620 (Y); -5467.650 (X)
Corner C coordinate = +3300.580 (Y); -5503.150 (X)

Calculate corner A's coordinates? I know how to calculate the area of a triangle by using the 3 coordinates, but for some or other reason the reverse of this equation doesn't work?

 

[phinds]

I've been away from math too long to actually sit down and DO this problem, but the one thing that you seem to be not understanding, based on your statement of the problem, is that there is no single coordinate. That is, the answer is not a coordinate. The answer is a function describing the locus of the 3rd coordinate, of which there are an infinite number (although they might be on a bounded curve).

 

[Jaynte]

If you know how to work with cross product you can use the formula:

$$Area=\frac{1}{2}|AB \times AC|$$

But the answer will be a function.