III. In the figure below, locate where dacoboa (P) is. Your illustration should contain the line segment mentioned in Definition 4.1.1. •P 45 60 Definition 4.1.1 Reflection in a line is the mapping defined by (P, if point P is on m, om (P)=Q.if P is off m and m is the perpendicular bisector of PQ Theorem 4.1.1 Reflection om is an involuntory transformation that interchanges the halfplanes of m. Reflection om fixes point P iff P is on m. Reflection om fixes line / pointwise iff !=m. Reflection om fixes line liff [= m or 11m. 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=¹ and op = 0p¹
III. In the figure below, locate where dacoboa (P) is. Your illustration should contain the line segment mentioned in Definition 4.1.1. •P 45 60 Definition 4.1.1 Reflection in a line is the mapping defined by (P, if point P is on m, om (P)=Q.if P is off m and m is the perpendicular bisector of PQ Theorem 4.1.1 Reflection om is an involuntory transformation that interchanges the halfplanes of m. Reflection om fixes point P iff P is on m. Reflection om fixes line / pointwise iff !=m. Reflection om fixes line liff [= m or 11m. 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=¹ and op = 0p¹
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:III. In the figure below, locate where acaba (P) is. Your illustration should contain the
line segment mentioned in Definition 4.1.1.
•P
پیکر
45
60
Definition 4.1.1 Reflection in a line m is the mapping defined by
(P, if point P is on m,
Om (P) = Q. if P is off m and
m is the perpendicular bisector of PQ
Theorem 4.1.1 Reflection om is an involuntory transformation that interchanges
the halfplanes of m. Reflection om fixes point P iff P is on m. Reflection om fixes
line / pointwise iff !=m. Reflection om fixes line liff 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:
0₁ = ¹ and op = 0p²
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