# What is the perpendicular distance between the parallel lines x - 2y = 8 and 2x - 4y = 9.

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The perpendicular distance between the lines x - 2y = 8 and 2x - 4y = 9 has to be determined.

The two lines can be written in the slope-intercept form as:

x - 2y = 8

=> y = x/2 - 4

2x - 4y = 9

=> y = x/2 - 9/4

The perpendicular distance between two parallel lines y = mx + b1 and y = mx + b2 is given by `D = |b2 - b1|/sqrt(m^2 + 1)`

Here, m = (1/2), b2 = -9/4 and b1 = 4

`D = |-9/4 + 4|/sqrt(1/4 + 1)`

= `7/(4*sqrt(5/4))`

= `7/(2*sqrt 5)`

**The perpendicular distance between the lines x - 2y = 8 and 2x - 4y = 9 is `7/(2*sqrt 5)` **