[Math] Find unknown vertex of triangle given area and other 2 vertices

Question

I need to find the coordinates of the 3rd vertex of a triangle given that I know the other 2 vertices and the area. The triangle is not guaranteed to be of any particular type (right, isosceles, acute, etc..).

Known vertex 1 will have coords (x1,y1)

known vertex 2 will have coords (x2,y2)

unknown vertex 3 will have coords (?, y2) or (x2, ?), in other words one part of the coordinate is the same as that in vertex 2.

Thanks

Answer 1

You're given one side, so you can calculate the length of that side. Next, you use the formula for area of a triangle to determine the height of the triangle. Finally, you set up the expression to calculate the distance from a point to a line using the known coordinate and the height you just calculated.