Question

Find the equations to the sides of an isosceles right-angled
triangle, the equation of whose hypotenuse is 3x + 4y = 4
and opposite vertex is the point (2,2).​

Answer 1

Answer:

7 y - x - 12 = 0 OR 7 x + y - 16 = 0

Step-by-step explanation:

Given :

Equation of line :

3 x + 4 y = 4

= > 3 x + 4 y - 4 = 0

Slope of line m = - A / B

m = - 3 / 4

Now we know :

tan Ф = ± ( m₁ - m₂ ) / ( 1 + m₁ m₂ )

Since straight line passing through given points ( 2 , 2 ) and making angle 45.

= > tan 45 = ± ( m₁ + 3 / 4  ) / (  1 - 3 / 4 m₁ )

= > m₁ = 1 / 7 or m₁ = - 7

Now required equation of two lines are as :

y - 2 = m ( x - 2 )

= > y - 2 = 1 / 7 ( x - 2 )

= > 7 y - x - 12 = 0

or

y - 2 = - 7 ( x - 2 )

= > 7 x + y - 16 = 0

Therefore we get required answer.