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The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle.

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. 

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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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