Question

I am a right isosceles triangle. I have an area of 50 square units. The coordinates of the vertex at which the two congruent sides meet is (0, 0) and my sides form horizontal and vertical lines. Do you have enough information to determine the coordinates of my two possible remaining vertices? I need two one for vertical side and one for the horizontal side.

Answer 1

The answer is yes. 
this is a right isosceles triangle, so it is a 45-45-90 triangle. From the given information, we know the origin (0,0) is the vertex where the 90 degree angles is. one leg is on the x axis, the other one the y axis. Note: the triangle can be in any of the four quadrants. x and y can be both positive and negative.

the area of the triangle is 50, A=half of leg * leg, since the two legs are of equal length, each leg is √100=10

There are four possibilities for the other two vertices:
first quadrant: (10, 0) , (0, 10)
second quadrant: (-10, 0) and (0, 10)
third quadrant: (-10, 0) and (0, -10)
fourth quadrant: (10, 0) and (0, -10)