TRANSFORMATIONS-COORDINATE RULES

TRANSFORMATIONS-COORDINATE RULES

These rules apply when the rotations are in counterclock-wise direction:

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REFLECTION RULES:

1.  x-axis.......(a, b) changes to (a,-b)

2. y-axis.......(a, b) changes to (-a,b)

3.  y=x .......(a, b) changes to (b, a)

4.  y=-x .......(a, b) changes to (-b, -a)

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             ROTATION RULES:

             5.  R₉₀  .......(a, b) changes to (-b, a)

             6. R₂₇₀  .......(a, b) changes to (b, -a)

             7. R₁₈₀  .......(a, b) changes to (-a, -b)

TRANSLATION RULES:

8.     P( x, y )-----P’( x + h , y – k )  means P moves h steps         to the RIGHT and P moves k steps DOWN.

9.    P( x, y )-----P’( x - h , y + k )  means P moves h steps          to  the LEFT and P moves k steps UP.

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10.  R_90°(x, y) ◦ T( x+h, y+k) ◦ r( x, y)_x-axis means ….first to reflect w.r.to x-axis; next translate to h units right and k units up; and finally rotate 90°.

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Try to Remember them.

Thanks.