Question

graphical problem:
The hypotenuse of right angled triangle has end points (1,3) and (-4,1). find the equation of the perpendicular sides(other two sides) of the triangle?

Answer 1

There are an infinite number of solutions to this question unless more information is given. A simple proposition in geometry states that if we consider the hypotenuse of a triangle as the diameter of a circle, then any triangle with its third vertex on the circle will be a right triangle. Notably, this means that we can pick the third vertex to be any other point (other than the two given, as this would form a degenerate triangle, aka a line segment) on the circle. Since the choice of the third vertex would determine the "equations" of the other two sides, there is no unique answer without more information.

Answer 2

use the equations of strait lines.

Answer 3

I assumed that's what you meant, but what I said still stands, there is not a unique solution to your problem. Consider the following drawing, where the hypotenuse is the diameter of the circle. Since any third point on the circle gives you a right triangle, there is no single solution to your problem. To convince yourself of this, choose any of the squares I placed on the circle. Note that each of these squares, if taken as the third vertex of the triangle will form a right triangle, and clearly all of these will have different equations for their sides.