Given: parallel lines 12x – 5y – 3 = 0, 12x – 5y + 7 = 0, 12x – 5y – 13 = 0

To Prove : line 12x – 5y – 3 = 0 is mid-parallel to the lines 12x – 5y + 7 = 0 and 12x – 5y – 13 = 0

Formula used :

The distance between the parallel lines ax + by + c =0 and ax + by + d =0 is,

D

The equation of line l is 12x – 5y + 7 = 0

The equation of line m is 12x – 5y – 3 = 0

The equation of line n is 12x – 5y – 13 = 0

Let D₁ be the distance between the lines l and m .

Here a = 12 ,b = -5 ,c = 7 ,d = -3

D_1..

The distance between the parallel lines l and m is units

Let D₂ be the distance between the lines m and n .

Here a = 12 ,b = -5 ,c = 7 ,d = -3

D₂

The distance between the parallel lines m and n is units

Distance between the parallel lines l and m = Distance between the parallel lines m and n

Thus the line 12x – 5y – 3 = 0 is mid-parallel to the lines 12x – 5y + 7 = 0 and 12x – 5y – 13 = 0