FIND THE DISTANCE BETWEEN PARALLEL LINES

If two lines are parallel, then they will have same slope. The equations of parallel lines will differ only by the constant.

To find the distance between parallel lines, we follow the procedure given below.

Step 1 :

Consider the first equation as Ax + By + C₁ = 0 and the second equations as Ax + By + C₂ = 0.

Since the given lines are parallel, they will differ only by the constant.

Step 2 :

If the coefficients of x and y are not same, make them as same and use the formula.

Step 3 :

|C1 - C2|/√A²+B²

Example :

Find the distance between the following pairs of parallel lines:

a) 3x - y + 2 = 0 and 3x - y + 8 = 0.

Solution :

3x - y + 2 = 0 ----(1)

3x - y + 8 = 0 ----(2)

A = 3, B = -1, C₁ = 2 and C₂ = 8.

Distance between the parallel lines :

= |2-8|/√[3²+ (-1)²]

= |-6|/√10

= 6/√10

So, the distance between the parallel lines is 6/√10 units.

b) 3x + 4y = 4 and 3x + 4y = 16.

Solution :

3x + 4y = 4 ----(1)

3x + 4y = 16 ----(2)

Here A = 3, B = 4, C₁ = 4 and C₂ = 16.

Distance between the parallel lines :

= |4-16|/√(3²+ 4²)

= |-12|/√(9 + 16)

= 12/√20

= 12/2√5

= 6/√5

So, the distance between parallel lines is 6/√5.

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