Question

Determine the distance between the lines:
a. 2x + 5y -10 =0 ; 4x + 10y + 25 = 0
b. 3x – 4y + 25 =0 ; 3x – 4y + 45 = 0

Just how?

Answer 1

@sammixboo

Answer 2

if both the lines have corresponding coefficients of x and y equal, we can apply the formula. Else, we’ll transform one of the equations by multiplying with some constant so that the coefficients become equal.

(i) 2x + 5y -10 =0 ; 4x + 10y + 25 = 0
As we can see coefficient of second equation is 2 times the first eq. Thus we will multiply first eq. by 2.
We get
4x +10y - 20 = 0 ; 4x + 10y + 25 = 0
Therefore, the required distance is equal to
\[|(-20)-(25)|\sqrt{4^2 + 10^2} = ?\]

(ii) 3x - 4y + 25 = 0 ; 3x - 4y + 45 = 0
As the coefficient of x and y are equal. Then the required distance is
\[|(25)-(45)|\sqrt{3^2 + (-4)^2} = ?\]