Perpendicular distance between two equations? (parallel)

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Homework Help Overview

The discussion revolves around finding the perpendicular distance between two linear equations, specifically y=2x-1 and y=2x-8/3. The problem is situated within the context of geometry and algebra, focusing on the properties of parallel lines.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the vertical distance between the y-intercepts of the two lines and suggest the use of a perpendicular line to determine the distance. Questions are raised about the properties of perpendicular lines and the geometric interpretation of the equations.

Discussion Status

The discussion is active, with participants providing guidance on how to approach the problem. Suggestions include finding a perpendicular line and determining the points of intersection with the original lines to calculate the distance. Multiple interpretations of the problem are being explored.

Contextual Notes

There is an emphasis on understanding the geometric implications of the equations rather than treating them as mere algebraic expressions. The distinction between the equations and their graphical representations is noted.

Dramacon
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Homework Statement


Find the perpendicular distance between y=2x-1 and y=2x - 8/3


2. The attempt at a solution
The first equation hits the y-axis at -1 and the other at -8/3, which means the vertical (y axis) distance between them is 5/3, but to use trig, I need another piece of information...this is where I am stuck... please help? :)
 
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Have you tried making a new line y_p perpendicular to both? The segment between the two y lines gives you your perpendicular distance.
 
Perpendicular distance between two equations? This depends upon where they are written on the page.

Now, to be serious ...

What is the slope of any line that's perpendicular to these two lines?
 
If SammyS hadn't beaten me to it, I would have said the same- "equations" are not geometric objects. You mean the distance between the two parallel lines that are the graphs, in a given coordinate system, of those two equations.

In any case, as both aeroplane and SammyS have said, find the equation of a line perpendicular to both lines. Find the two points where this third line crosses the two given lines and find the distance between those two points. Since that distance will be the same for any such perpendicular, you can choose whatever point you want for the line to go through.
 

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