Question

If one of the diagonal of a square is along the
line x = 2y and one of its vertices is (3, 0)
then its sides through this vertex are given by
the equations

Answer 1

equation of line will be

Answer 2

As A(3,0) does not satisfy the diagonal x=2y, 

⇒A(3,0) does not lie on the diagonal x=2y.

Let m be the slope of a side passing through A(3,0),

⇒ equation of the side is : y−0=m(x−3),

⇒y=m(x−3)−−−−−−EQ1,

Formula to find the angle between two lines :

tanθ=∣∣∣m1−m21+m1m2∣∣∣,

Where θ is the angle between the two lines

and m1andm2 are the slope of the two lines.

Slope of the diagonal x=2y is 12

⇒tan45=∣∣ ∣∣m−121+m⋅12∣∣ ∣∣
⇒1=∣∣ ∣∣m−121+m2∣∣ ∣∣
⇒m=3or−13

Substituting m=3,and−13 in EQ1, we get :

y=3(x−3),⇒y−3x+9=0,
and,
y=−13(x−3),⇒3y+x−3=0