254 NEW MODE OF REPRESENTING 



Determine the equation to the line A CB where 

 A C and CB are the sides of an isosceles 

 triangle. 



Taking the point 

 A for the origin of 

 co-ordinates, and call- 

 ing the hypothenuse 

 AB = 2 A 



We have for the equation of AC, y — x 



Do. BC, y-2- X 



Therefore, we have 



y zz .r, between the limits .v = and .v — 1 



and 



y^2 - X, between the limits x = 1 and x = 2 



consequently, 



a = 1 and f (.r) = x and f, (.r) - 2 - x 



Substitute these values in equation (1) art. 10, 

 and we shall have — 



