Question

Find the distance between the two lines x+y=2 and 2x+2y=6

Answer 1

The given lines are parallel lines.

First, make the coefficient of x and y equal as below:

Divide the equation by 2 to get the coefficient of x and y equal to 1

i.e. x+y=3

Now, use the formula of distance between the two parallel lines given below:

Distance= mode(C1-C2)/(a^2+b^2)^(1/2) where C1 and C2 are constant, a and b are coefficient of x and y respectively.

So, we have

Distance= mode(3-2)/(1^2+1^2)^(1/2)=1/2^(1/2)

Rationalizing the answer, we get

2^(1/2)/2

Therefore, the distance between the given lines=2^(1/2)/2