Algebra to describe Geometry 2
The coordinates of point (x, y) after a counterclockwise rotation about the origin become (-y, x) :
the coordinates of point (2, -3) after a counterclockwise rotation about the origin are (-(-3), 2) =(3, 2)
ReflectXXX y-axis : (x, y) -> (-x, y)
XXXXXXXX of XXXo about the origin : (x, y) -> ( -x, -y)
XXXXXXXXXXXmunits XXXXX : (x, y) -&XX; ( x+m, y)
XXXXXXXX XX 90o about XXXXXXX-clockwise XXX XXXXXX : (x, y) -&XX; ( -y, x)
∆ABC XXXXXXXX XX 90o XXXXXXXXXXXXXXXX 2 units right ∆A’X’X’
XXXXXXX-XXXXXXXXX
XXX origin
(x, y)(-y, x)(-y+2, x)
X(-4, 3)(-3, -X)( -3+X, -4) A’(-1,-X)B(-1, X)(-X, -X)(-X+X, -1)B’(-2, -1)X(-2, X)(-X, -X)(-X+X, -2) C’( X, -X)
The sequence of XXXXXXXXXXXXXXX XXXX maps ∆XXX XX ∆A’X’X’ isrotation XX 90o XXXXX counter-clockwise XXX XXXXXXXXXXXXXX bytranslation X XXXXX XXXXX.
(x,y) -&XX; (y,x) : Reflection XX (x,y) XXXXXX the line y=x
The vertices of XXX XXXXXXXXX XXX (X,X), (X,X),XXX (8,1)
XXXXX XXX transformation XXX XXXXXXXX are(6,8), (X,5) XXX (X,8)
(x,y) -&XX; (x+X, y-X) : Translation of (x,y) to 3XXXXX left XXX 5units down.
The XXXXXXXX of the XXXXXXXX are (X,7), (2,X), and (X,-X)
XXXXX XXXXXXXXXXX XXX vertices are(X,2), (5,-X) and ( 7,-8)
XXXXXXXXXXXm XXXXX XXXX : (x,y) -&XX; ( x-X, y )
Reflection across the x-XXXX : (x,y) -> ( x,-y )
Reflection across the y-XXXX : (x,y) -&XX; ( -x,y )
XXXXXXXXXXXn units XXXX : (x,y) -> ( x, y-n )
Vertices of ∆XXX : A(-4, X)X( -X, X)C (-X, 2)
XXXXXXXXXX XXXXXX y-axis : ( 4, X ) ( X, X ) ( X, X)
Translate X units XXXX: (X-X, 6) (X-2, X ) ( X-X, 2)
Vertices of ∆X’X’X’ : A’( X, X )B’( X, X )C ‘( X, 2 )
XXX XXXXXXXX XX XXXXXXXXXXXXXXX XXXX XXXX ∆XXX XX ∆A’X’X’ isreflection across y-axis XXXXXXXX byXXXXXXXXXXX 2 units left.
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