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12.9 Applying the distance formula to a triangle (a) Find the lengths of the sides of a triangle whose vertices are A(1, 1), B(1, 4), and C(5, 1). (b) Show that the triangle whose vertices are G(2, 10), H(3, 2), and J(6, 4) is a right triangle.

See Fig. 12-9.

6

y G(2,10)

Fig. 12-9

( (2

3)2 3)

5. (10 2)2



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To use SAX to read XML, you create an instance of a parser object that is pointed to your document and to your application While SAX reads the document, it calls the startElement (the start tag), endElement (the end tag), and characters (text data in between) as it goes The SAX parser reads the XML le (also a DTD if it is present), and when it encounters something such as an element, it generates an event On recognition of such an event, your program can register with the parser as a listener by implementing certain interfaces The SAX parser then calls certain methods, which you have overridden to do what you need to do in response to the event Although the SAX parser organizes its events a bit di erently, the situation is similar to an Abstract Window Toolkit (AWT) button generating ActionEvents when clicked.

13; (GH)

In This :





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12.10 Applying the distance formula to a parallelogram The coordinates of the vertices of a quadrilateral are A(2, 2), B(3, 5), C(6, 7), and D(5, 4). Show that ABCD is a parallelogram.

See Fig. 12-10, where we have AB CD BC AD 2(3 2(6 2(6 2(5 2)2 5)2 3)2 2)2 (5 (7 (7 (4 2)2 4)2 5)2 2)2 212 212 232 232 32 32 22 22 210 210 213 213

C(6, 7)

Fig. 12-10

12.11 Applying the distance formula to a circle A circle is tangent to the x-axis and has its center at (6, 4). Where is the point (9, 7) with respect to the circle

Since the circle is tangent to the x-axis, AQ in Fig. 12-11 is a radius. By Principle 2, AQ By Principle 3, BQ 2(9 6)2 (7 4)2 greater than a radius so B is outside the circle. 232 32 4. 218. Since 218 is greater than 4, BQ is

y B(9, 7)

Introduction Special Ledgers Sales Returns and Discounts Types of Ledger Account Forms Purchases As a Cost Trade Discounts Purchase Control Purchase Invoices Purchases Journal Subsidiary Accounts Payable Ledger 33

Q(6, 4)

x O y A(6, 0)

Fig. 12-11

PRINCIPLE 1:

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PRINCIPLE 2: PRINCIPLE 3:

The inclination i of a line is the angle above the x-axis that is included between the line and the positive direction of the x-axis (see Fig. 12-12). In the figure,

Summary

The slope is independent of the order in which the end points are selected. Thus, y2 x2 y1 x1 y1 x1 y2 x2

Then an interested class implements an ActionListener and overrides the callback method actionPerformed SAX events, unlike AWT events, come in an ordered sequence as the XML le is read in Given the tree structure of the XML le, the parser generates events in a depth- rst order Furthermore, because the events are triggered on the y as the XML le is read in, you only get one chance to grab an event as it goes by You must do something to capture relevant information at the point at which it arrives, or the information is lost unless you parse the entire le again This is in contrast to the DOM parser, which reads the entire document in, storing it in its tree structure in memory, and then waits for your program to analyze it The steps are 1 2 3 4.

Fig. 12-12

PRINCIPLE 4:

If a line slants upward from left to right, its inclination i is an acute angle and its slope is positive (Fig. 12-13).

Fig. 12-13

Fig. 12-14

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