Describe the Locus
Date: 03/28/2002 at 02:01:00 From: Andrea Subject: Geometry Describe in words the locus that satisfies the given condition. What is the locus of all points in a plane two inches from a point A? I took the basic information from the book regarding this, but I don't know if this is correct because they haven't given me any condition. RESOLUTION: The locus is the circle with the center P and radius of 1cm. The locus is the sphere with the center P and radius of 2". Thanks for your help; it is greatly appreciated.
Date: 03/28/2002 at 12:33:15 From: Doctor Peterson Subject: Re: Geometry Hi, Andrea. I'm not sure what you mean by saying they haven't given a condition; the condition is that the points are 2 inches from A. Since you are in a plane, the answer can't be a sphere. But a circle with radius 2 inches (not 1 centimeter!) will fit the description. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 03/28/2002 at 21:45:07 From: Andrea Subject: Geometry Sorry, I can't draw very well with the computer yet. It is actually a circle with an x at the top of the circle and the number two is inside on the left-hand side. The degrees are located outside the circle. Hope I'm explaining this right. Thanks.
Date: 03/28/2002 at 22:53:23 From: Doctor Peterson Subject: Re: Geometry Hi, Andrea. Actually, it's better to describe a geometrical figure in words than to draw it - thinking about how to say it often helps you understand the problem better. Here's my version: ooooooooooooo o+ooo +ooooo oo \ / oo ooo \ / ooo 40 o \ / o oo 2 X oo 60 o / \ o o / \ o o / \ o o / \ o o / \ o o / \ o o / \ o o / \ o + \ o o \ o o + oo oo o o ooo ooo oo oo ooooo ooooo ooooooooooooo I presume the 40 and 60 are the measures of the arcs, that is, their central angles. The formula here is angle 2 = (40 + 60)/2 If you forget this, you can draw an extra line and use the simpler fact that an inscribed angle is half the central angle of the arc it subtends: ooooooooooooo o+ooo +ooooo oo \ / oo ooo \ / ooo o \ / o a oo x X oo o / \ o b o / \ o o / \ o o / \ o o / \ o o / \ o o / \ o o / z \ o A+--------________ \ o o -------________ y \ o o ---------+B oo oo o o ooo ooo oo oo ooooo ooooo ooooooooooooo Then y = a/2 and z = b/2, and x, an exterior angle of triangle AXB, is the sum, x = y+z = (a+b)/2. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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