the hypotenuse of aright triangle has endpoints (1,3) &(-4,1) find the equation of other two sides?

Question

give the method

Answer 1

There are an infinite number of right angled triangles that could be constructed with that line as the hypotenuse. The locus of the other point of the triangle will be a circle with its centre at the midpoint of the hypotenuse and diameter as the length of the hypotenuse.

The other two sides will be chords of the circle. You will first need to determine the equation for the locus of a point on the circle and then use this in two equations which will show the slope and offset of the two chords for any position of the point on the circle.

If you are looking for the special case solution where the sides are parallel to the axes, there are two answers, of course, depending on which side of the hypotenuse you choose to draw the right angle.

If you drop a vertical line, parallel to the y axis through a point (n,m), it's equation will simply be x = n. Likewise, drawing a horizontal line, parallel to the x axis, the equation will be y = m

Applying that to the end points of your hypotenuse you have either:

x=1 and y=1

or

x = -4 and y = 3

I find that it always helps to draw a rough sketch, mark the points given and then construct the triangles.

Answer 2

x=1 and y=1

Answer 3

1,1 or 4,3