Distance between Point and LineDate: 02/08/2009 at 10:47:27 From: Lucy Subject: Distance from lines What distance is the point (1,2) from the line 3x + 6y = 10? I know how to draw the line and how to plot points but I don't know how to find the closest distance in between points. Date: 02/11/2009 at 09:35:21 From: Doctor Ian Subject: Re: Distance from lines Hi Lucy, Let's start there, then. Suppose you plot the line A, 3x + 6y = 10 and the point P, at (1,2). Now draw any line B through P that will intersect A at point Q. You might get something like \ / \ / \ A P \ / \ / \ / B \ / Q / \ / \ / \ So far, so good? Now, for any line you choose, there will be some distance from P to Q. There is ONE line that will give you the SHORTEST possible distance. Which one? The one that is perpendicular to A. \ \ \ A P \ . \ . \ . B \ . Q . \ . \ \ Make sure you understand WHY this is true before going on. If it's not clear, let me know. In the case where we have the perpendicular line, the distance from P to Q is considered to BE the distance from the point to the line-- because there is no other possible distance that could be smaller. If that all makes sense, then you can rephrase the problem this way: If A is the line 3x + 6y = 10, and P is the point (1,2), and B is a line perpendicular to A and passing through P, find the distance from P to the point where A intersects B. Here's something you'll want to know: If two lines are perpendicular (and neither is vertical), the product of their slopes is -1. Is this enough to get started? Let me know if you need more help. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 02/11/2009 at 21:12:39 From: Lucy Subject: Thank you (Distance from lines) Thank you so much for your help. Your explanation was perfect and my understanding is complete. |
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