Question

Find the equation of one of the sides of an isosceles right angled triangle whose

hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).

Answer 1

Toolbox:

Slope of a line is m=−coeffofxcoeffofy

tanθ=∣∣∣m1−m21+m1m2∣∣

Step 1 :

The equation of the hypotenuse is 3x+4y=4 .

Hence the slope of the line is −34

ASince it is an isoceles right angled triangle the angles should be 45∘,45∘ and 90∘

tan45∘=∣∣∣m−(−34)1+m(−34)∣∣

But tan45∘=1

1=∣∣∣m+341−3m4∣∣

1−3m4=±(m+34)

Step 2 :

If 1−3m4=m+34

⇒m+3m4=1−34

7m4=14

∴m=17

The coordinates of B is (2,2)

Hence the equation of the line AB is

(y−2)=17(x−2)

7y−14=x−2

∴x−7y=−12

Hence x−7y+12 is the required equation.