Divide the difference between the values of the y coordinates and those of the x coordinates. If your coordinates are A (4, 0) and B (2, 8), subtract 8 from 0, then 2 from 4. Divide the result from the y coordinates by the results obtained from the x coordinates. In this case, the solution is -8 divided by 2, which gives -4. This is the slope or gradient of the line joining the two coordinates. Mathematicians usually refer to the gradient as "m."
Multiply the value of m by either of your two x coordinates, then subtract the y coordinate of the same point to get the y intercept of the line, known as "b." In this case, the value you obtain is -16.
Find the perpendicular to the line adjoining the two coordinates. This is easy if you know that the product of gradients of two perpendicular lines gives -1. In this case, since the initial gradient was -4, the gradient of the perpendicular to this line becomes ¼. Find the equation of the perpendicular line by replacing values of any of the points.
Use Pythagoras's theorem to calculate the distance between the two coordinates. To do this, subtract the value of the x coordinates, then subtract the values of the y coordinates. Square the two results, then add them together. Find the square root of the value obtained from the addition. In this case, the answer is approximately 8.25.
Subtract the two values for x and those for y again. Divide each result independently by two. In doing so, you are finding the midpoint of the line joining the two coordinates. In this example, the mid-coordinate is M (2,-4).
Draw a circle centered at the mid coordinate, using a compass. This circle gives all possible points where the third vertex of the triangle can lie. Construct an orthogonal line to the line adjoining the two coordinates, taking the midpoint as your reference point. Make sure the orthogonal passes through the circle. Choose any point on either side of the circle and join the known coordinates to it. You now have the third vertex of your triangle.