# Q : 17     The hypotenuse of a right angled triangle has its ends at the points  $\small (1,3)$  and  $\small (-4,1)$  Find an equation of the legs (perpendicular sides) of the triangle.

Slope of line OA and OB are negative times inverse of each other
Slope of line OA is  ,  $m=\frac{3-y}{1-x}\Rightarrow (3-y)=m(1-x)$
Slope of line OB is , $-\frac{1}{m}= \frac{1-y}{-4-x}\Rightarrow (x+4)=m(1-y)$
Now,

Now, for a given value of  m we get these equations
If $m = \infty$
$1-x=0 \ \ \ \ and \ \ \ \ \ 1-y =0$
$x=1 \ \ \ \ and \ \ \ \ \ y =1$

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