Given 2 points, what is the third point on the y-axis to create a right triangle? I am given points A:(4, -2) and B:(-4, 4) to find all the points to make right triangle ABC
I understand that there are 4 different points and that the third point is (0, y). I also understand there are two processes to find 2 points each. What do I have to do to solve all 4 points?
 A: Now find the middle point of the line segment joining the given points. Draw a circle having center at the middle point and of radius half of the length of the line segment. Every point on the circle is your required point by which you can make a right angle triangle. That will make $ACB$ as a right angle triangle.
To form $ABC$ right angle triangle draw a perpendicular of $AB$ at $B$, extend the line and pick any point $C$ on the new line, join $C$ with $A$ and we are done with $ABC$ right angle triangle.
A: A visual version of the method:

We start with a segment $AB$ and wish to find points on a given line making a right triangle with $AB$. Those points are the red dots, where the perpendiculars to $AB$ through $A$ and $B$ and the circle with diameter $AB$ meet the line.
(The particular choices in this picture put the midpoint of $AB$ on the line. That's not necessary in general.) 
A: The dot product of pairs of vectors will equal 0, if they meet at right angles.
$(Y_1 - A)\cdot (B-A) = 0\\
(Y_2 - B)\cdot (B-A) = 0\\
(Y_3 - A)\cdot (Y_3-B) = 0$
And the last one will give you two results
