Answer :

Given: hypotenuse is 3x + 4y = 4 of isosceles right angled triangle the opposite vertex is the point (2, 2).


To find: equation of side of isosceles right angle triangle


Explanation:


Here,


we are given ABC is an isosceles right angled triangle .


A + B + C = 180°


90° + B + B = 180°


B = 45°, C = 45°


Diagram:



Now, we have to find the equations of the sides AB and AC, where 3x + 4y = 4 is the equation of the hypotenuse BC.


We know that the equations of two lines passing through a point x1,y1 and making an angle α with the given line y = mx + c are



Here,
Equation of the given line is,


3x + 4y = 4


4y = - 3x + 4



Comparing this equation with y = mx + c


we get,



x1 = 2, y1 = 2,
α = 45, m


So, the equations of the required lines are





x – 7y + 12 = 0 and 7x + y – 16 = 0


Hence, Equation of given line is x – 7y + 12 = 0 and 7x + y – 16 = 0


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