Question 1060895: If the length of th hypotenuse triangle is 17 units and the legs lie along the x axis and y axis, find a possible equation that describes the line that contains the hypotenuse
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! An ordered set of 3 integers that could be the shorter leg, the longer leg, and the hypotenuse of a right triangle is called a Pythagorean triple.
If you search omline for a list of Pythagorean triples,
you will find the triple (8,15,17),
meaning that a right triangle with legs measuring 8 and 15 has a hypotenuse of length 17.
The list does not have another Pytahgorean triple ending in 17, so there are four possible looks for the triangle, and in all cases the numbers  and  will appear in the equation of the line that contains the hypotenuse.
with the legs along the axes, the right angle would be at the origin,  ,
The triangle could look like POR below, with the long leg parallel along the x-axis, and the right angle on the bottom, right end
 . The hypotenuse would have a slope of  ,
The x- and y-intercepts would be P and R respectively, and the equation of the line containing the hypotenuse would be
 <-->  .
Flipping the triangle twice, to get  and  ,
yields  <-->  , with the same slope
If the triangle were flipped once, with and  , or  and ,
the slope would be 
the equation of the line containing the hypotenuse would be
 <-->  or
 <-->  .
With the long side on the y-axis, the slopes would be  or  ,
and the equations would have  ,  ,  ,  .
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