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A dihilation (also called a scaling or an enlargement) is not a rigid motion because it multiplies all lengths by a single scale factor. The image of a figure under a dihilation will always be similar to the original. The dihilation that enlarges everything by a scale factor of k is P(x, y) A Pr(kx, ky).

18.17 Performing dihilations Let triangle ABC be formed by A(2, 2), B(4, 2), and C(4, 3). Graph the image of ^ABC under 1 (a) magnification by 2 and (b) scaling by 2.



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others. It is incorporated into many operating systems and all modern browsers, as well as database tools (such as MS SQL Server, Oracle, and Sybase) and programming languages (such as Java, Perl, and Visual Basic). Unicode is required by new technologies developed by such industry giants as the W3C, the Internet Engineering Task Force (IETF), and the Object Management Group (OMG). Examples are XML, XHTML, XSL, the Lightweight Directory Access Protocol (LDAP), and the like. UTF-8 is the most widely understood Unicode format and is the default encoding set for many programs that claim to use Unicode. In XML, however, the character set can be speci ed, the most common being UTF-8 or UTF-16. Table 1-2 provides some Unicode characters with their Windows and HTML encoding.

See Fig. 18-16.

Fig. 18-16

(a) Ar(4, 4), Br(8, 4), and Cr(8, 6) (b) As(1, 1), Bs(2, 1), and Cs(2, 1.5)

16





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18.18 Naming dihilations Name the transformation that (a) Scales everything 5 times larger (b) Shrinks every length to half size (c) Triples all linear dimensions (d) Depicts everything at 10 scale (e) Dihilates by a scale factor of 12

(a) P(x, y) A Pr(5x, 5y)

1 1 (b) P(x, y) A Pr(2x, 2y)

(c) P(x, y) A Pr(3x, 3y)

1 1 (d) P(x, y) A Pr(10x, 10y)

(e) P(x, y) A Pr(12x, 12y)

In This :

18.1. Name the image of points A(6, 2), B( 1, 4), and C(2, 7) under the transformation (a) P(x, y) A Pr(x (b) P(x, y) A Pr(2 (c) P(x, y) A Pr( x (d) P(x, y) A Pr( y, x (e) P(x, y) A Pr(2x, 2y) (f) P(x, y) A Pr(4 (g) P(x, y) A Pr(2 3x, 3y) y, 5 x) 1), B(2, 2), and C(3, 1). Graph the image of ^ABC under 3, y) x, y) 1, 8) y 3)

18.2. Let triangle ABC be defined by A(1, (a) P(x, y) A Pr(x (b) P(x, y) A Pr(x, y (c) P(x, y) A Pr(x 18.3. 5, y) 4) 3, y 2)

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Name the translation that takes ^ABC to (a) ^ArBrCr, (b) ^AsBsCs, and (c) ^A-B-C- as illustrated in Fig. 18-17.

Fig. 18-17

The size of an angle depends on the extent to which one side of the angle must be rotated, or turned about the vertex, until it meets the other side. We choose degrees to be the unit of measure for angles. The measure of an angle is the number of degrees it contains. We will write m/A 60 to denote that angle A measures 60 . S The protractor in Fig. 1-9 shows that /A measures of 60 . If AC were rotated about the vertex A until it S met AB , the amount of turn would be 60 . In using a protractor, be sure that the vertex of the angle is at the center and that one side is along the 0 180 diameter. The size of an angle does not depend on the lengths of the sides of the angle.

Fig. 1-9

Table 1-2 Windows ALT-0130 ALT-0131 ALT-0132 ALT-0133 ALT-0134 ALT-0135 ALT-0136 ALT-0137 ALT-0138 ALT-0139 ALT-0140 ALT-0145 ALT-0146 ALT-0147 ALT-0148 ALT-0149 Sample Unicode Characters with Windows and HTML Equivalents HTML ‚ ƒ „ … † ‡ ˆ S ‰ Š ‹ Œ ‘ ’ “ ” • Character Test

Fig. 1-10

Characteristics Formation of the Partnership Division of Net Income and Loss Admission of a New Partner Liquidation of a Partnership Summary Solved Problems

The size of /B in Fig. 1-10 would not be changed if its sides AB and BC were made larger or smaller. No matter how large or small a clock is, the angle formed by its hands at 3 o clock measures 90 , as shown in Figs. 1-11 and 1-12.

Fig. 1-11

Fig. 1-12

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