My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum

LinkBack Thread Tools Display Modes
July 1st, 2015, 07:33 PM   #1
Joined: Jul 2015
From: US

Posts: 2
Thanks: 0

Parallel line calculations???

I have a set of lines where I know the beginning and end coordinates (X1, Y1, X2, Y2). What I need to calculate is a set of begin/end coordinates for parallel lines that makes the line a set distance away.

Example, if I have coordinates (0,0,50,0), which is a horizontal line, and the distance required is 10, then what I should end up with is (0,10,50,10) a line that is parallel to the first but offset by 10. I plan to put in +10 and -10 for the distances to get lines the same distance on either side.

How would I go about that?
LadyLisa is offline  
July 2nd, 2015, 04:13 AM   #2
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,237
Thanks: 884

For non-horizontal and non-vertical lines, the calculation is quite a lot more tedious. Suppose you have a line with one point $\displaystyle (x_0, y_0)$ and another point [math](x_1 , y_1)[math] (I would not say "end points"- lines do not have ends). You need to find a line perpendicular to that line at each point. The given line has slope $\displaystyle \frac{y_1- y_0}{x_1- x_0}$. Any line perpendicular to that given line must have slope $\displaystyle \frac{x_0- x_1}{y_1- y_0}$. A line through $\displaystyle (x_0, y_0)$ perpendicular to that given line has equation $\displaystyle y= \left(\frac{x_0- x_1}{y_1- y_0}\right)(x- x_0)+ y_0$. Now you will have to use the distance formula to find a point on this new line at the desired distance from $\displaystyle (x_0, y_0)$. Do the same with point $\displaystyle (x_1, y_1)$.
Country Boy is offline  

  My Math Forum > High School Math Forum > Geometry

calculations, line, parallel

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Point at which tangent line is parallel to secant? jaredbeach Calculus 4 May 12th, 2017 09:47 AM
Proving planes intersect in line or are parallel Limittox Geometry 2 April 12th, 2015 03:01 PM
finding equation of line that is parallel to intersection... jmorris Pre-Calculus 4 November 19th, 2014 05:54 PM
Steiner construction of a parallel line tx3 Algebra 4 May 23rd, 2013 11:47 PM
points on curve parallel to line fran1942 Calculus 5 April 2nd, 2012 08:48 PM

Copyright © 2018 My Math Forum. All rights reserved.