Lines

[kathryn.elizabeth531]

How do you find the perpindicular distance between two lines?
Do you use the distance formula, and if so what two points would you use?

The lines are
y = 2x + 7
and
y = 2x + 2

Since the lines have the same slope, they are parallel but I'm unsure how to find the distance. I don't need to know the answer, just how to solve it, specifically equations to use or formulas.

Thank you.

 

[Loren]

One approach might be to come up with the equation of a line that is perpendicular to the two given lines. Just any line will do, so long as it is perpendicular to the given lines. We know that the slope of this perpendicular line will be the negative reciprocal of the slope of the given lines. After you have this third line, find the points where it intersects the given lines and use the distance formula. So, I guess you could solve two sets of simultaneous equations, one set consisting of the third line and one of the original lines and the other consisting of the third line and the other original line. That will give you the two points to use in the distance formula.