Reflection: its concepts and applications in geometry - ResearchGate
Reflection: its concepts and applications in geometry - ResearchGate
Reflection: its concepts and applications in geometry - ResearchGate
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Asia-Pacific Forum on Science Learn<strong>in</strong>g <strong>and</strong> Teach<strong>in</strong>g, Volume 5, Issue 3, Article 7, p.8 (Dec., 2004)<br />
MAN Yiu Kwong<br />
<strong>Reflection</strong>: <strong>its</strong> <strong>concepts</strong> <strong>and</strong> <strong>applications</strong> <strong>in</strong> <strong>geometry</strong><br />
Figure 10<br />
A further exploration by dynamic <strong>geometry</strong> software also reveals that the mirror<br />
image of D 1 with respect to BC, say D 3 , must lie on the extension of D 2 Q. It is<br />
because ∠PQB = ∠D3QB = ∠RQC, <strong>and</strong> so D 2 , Q <strong>and</strong> D 3 are coll<strong>in</strong>ear, as shown<br />
<strong>in</strong> Figure 11. Hence, we know that a quick solution to this billiard ball problem is to<br />
f<strong>in</strong>d the mirror images D 1 , D 2 <strong>and</strong> D 3 first, <strong>and</strong> draw the l<strong>in</strong>e segment D 2 D 3 to locate<br />
the positions of R <strong>and</strong> Q, <strong>and</strong> then draw the l<strong>in</strong>e segment D 1 Q to locate the position of<br />
P. Jo<strong>in</strong><strong>in</strong>g the po<strong>in</strong>ts D, P, Q <strong>and</strong> R will give us the path required.<br />
Figure 11<br />
Copyright (C) 2004 HKIEd APFSLT. Volume 5, Issue 3, Article 7 (Dec., 2004). All Rights Reserved.
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