Difference between revisions of "Reflection"
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It is also possible to have reflection about a point. This is essentially a [[rotation]] of <math>180^{\circ}</math>. To do this, suppose we have triangle <math>ABC</math> and wish to rotate it around point <math>O</math>. Draw <math>OA</math>. Then, double its length so that it reaches point <math>A'</math>, such that <math>O \in</math> segment <math>AA'</math>, and <math>OA=OA'</math>. Do this for the other points to get reflected triangle <math>A'B'C'</math>. | It is also possible to have reflection about a point. This is essentially a [[rotation]] of <math>180^{\circ}</math>. To do this, suppose we have triangle <math>ABC</math> and wish to rotate it around point <math>O</math>. Draw <math>OA</math>. Then, double its length so that it reaches point <math>A'</math>, such that <math>O \in</math> segment <math>AA'</math>, and <math>OA=OA'</math>. Do this for the other points to get reflected triangle <math>A'B'C'</math>. | ||
<math>A',B',</math>and<math>C'</math> are now said to be symmetric to <math>A,B,</math> and <math>C</math> respectively, with respect to <math>O</math>. (Pardon the pun.) | <math>A',B',</math>and<math>C'</math> are now said to be symmetric to <math>A,B,</math> and <math>C</math> respectively, with respect to <math>O</math>. (Pardon the pun.) | ||
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Revision as of 00:12, 21 May 2013
A reflection is basically like flipping a planar figure over a mirror. The figure has the same shape and size, except it is facing the opposite direction. When working in two dimensions, you can use a line as the "mirror". Once we reflect a figure across this line, we will find that every point is symmetric to its reflection with respect to the line. This means that, if you folded the paper over the line, the two figures would line up. Therefore, any point on the original is the same distance from the line of reflection as its reflection is.
It is also possible to have reflection about a point. This is essentially a rotation of 
. To do this, suppose we have triangle 
and wish to rotate it around point 
. Draw 
. Then, double its length so that it reaches point 
, such that 
segment 
, and 
. Do this for the other points to get reflected triangle 
.
and
are now said to be symmetric to 
and 
respectively, with respect to . (Pardon the pun.)
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