1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Shortest distance between two points (one unknown?)

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Find an equation of the line, say y=mx+b, which passes through the point (6,−2) and is perpendicular to the line −2x+4y=0

    y=

    What is the shortest distance from the point (6,−2) to the line −2x+4y=0?

    2. Relevant equations

    ?

    3. The attempt at a solution

    So I found the equation of the line - 4y = 2x, y = 1/2x so the slope of the line it is perpendicular to is 1/2. So the line in question has a slope of -2. Subbed in the point (6,-2) and the slope to solve for b, and came up with the equation y = -2x + 10. Now I'm stumped on the second part of the question. I know the distance formula but how do I figure out the second point?

    Thanks
     
  2. jcsd
  3. Sep 12, 2009 #2
    Imagine a point somewhere above a line, say the x-axis. Imagine different lines going from the point to different points on the x-axis. Which one of those will be the shortest distance between the point and the x-axis? What's the relationship between their slopes?
     
  4. Sep 12, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The "shortest distance" from a point to a line is always perpendicular to that line. Where does your line y= -2x+ 10 intersect y= (1/2)x?
     
  5. Sep 12, 2009 #4
    Thanks for the help. I got the answer, my graphing calculator was throwing me off for some reason.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Shortest distance between two points (one unknown?)
Loading...