III. In the figure below, locate where daca(P) is. Your illustration should contain the line segment mentioned in Definition 4.1.1. 60

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Chapter10: Rounding Decimal Fractions And Equivalent Decimal And Common Fractions
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III. In the figure below, locate where (P) is. Your illustration should contain the
line segment mentioned in Definition 4.1.1.
45
60
b
Transcribed Image Text:III. In the figure below, locate where (P) is. Your illustration should contain the line segment mentioned in Definition 4.1.1. 45 60 b
4.1 Equations for a Reflection
Definition 4.1.1 Reflection in a line is the mapping defined by
(P, if point P is on m,
am (P) = Q. if P is off m and
m is the perpendicular bisector of PQ
Theorem 4.1.1 Reflection
is an involuntory transformation that interchanges
the halfplanes of m. Reflection om fixes point P iff P is on m. Reflection of fixes
line / pointwise iff !=m. Reflection om fixes line / iff 1 = m or l 1 m.
Remarks:
1. A halfturn is a sort of "reflection in a point", although we shall never use this
terminology to avoid confusion.
2. The similar notation for halfturns and reflections emphasizes the important
property they do share, namely that of being involutions:
= ¹ and = 0p¹
Transcribed Image Text:4.1 Equations for a Reflection Definition 4.1.1 Reflection in a line is the mapping defined by (P, if point P is on m, am (P) = Q. if P is off m and m is the perpendicular bisector of PQ Theorem 4.1.1 Reflection is an involuntory transformation that interchanges the halfplanes of m. Reflection om fixes point P iff P is on m. Reflection of fixes line / pointwise iff !=m. Reflection om fixes line / iff 1 = m or l 1 m. Remarks: 1. A halfturn is a sort of "reflection in a point", although we shall never use this terminology to avoid confusion. 2. The similar notation for halfturns and reflections emphasizes the important property they do share, namely that of being involutions: = ¹ and = 0p¹
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