(Geometry: point position) Programming Exercise 3.32 shows how to test whether a point is on the left side of a directed line, on the right, or on the same line. Write the methods with the following headers:

/** Return true if point (x2, y2) is on the left side of the
* directed line from (x0, y0) to (x1, y1) */
public static boolean leftOfTheLine(double x0, double y0,
double x1, double y1, double x2, double y2)

/** Return true if point (x2, y2) is on the same
* line from (x0, y0) to (x1, y1) */
public static boolean onTheSameLine(double x0, double y0,
double x1, double y1, double x2, double y2)

/** Return true if point (x2, y2) is on the
* line segment from (x0, y0) to (x1, y1) */
public static boolean onTheLineSegment(double x0, double y0,
double x1, double y1, double x2, double y2)

Write a program that prompts the user to enter the three points for p0 , p1 , and p2 and displays whether p2 is on the left side of the line from p0 to p1 , right side, the same line, or on the line segment. Here are some sample runs:

Enter three points for p0, p1, and p2: 1 1 2 2 1.5 1.5
(1.5, 1.5) is on the line segment from (1.0, 1.0) to (2.0, 2.0)

Enter three points for p0, p1, and p2: 1 1 2 2 3 3
(3.0, 3.0) is on the same line from (1.0, 1.0) to (2.0, 2.0)

Enter three points for p0, p1, and p2: 1 1 2 2 1 1.5
(1.0, 1.5) is on the left side of the line
from (1.0, 1.0) to (2.0, 2.0)

Enter three points for p0, p1, and p2: 1 1 2 2 1 –1
(1.0, −1.0) is on the right side of the line
from (1.0, 1.0) to (2.0, 2.0)

Given a directed line from point $p0(x0, y0)$ to $p1(x1,y1)$, you can use the following condition to decide whether a point $p2(x2, y2)$ is on the left of the line, on the right, or on the same line.

$$(\mathrm{x} 1-\mathrm{x} 0)^*(\mathrm{y} 2-\mathrm{y} 0)-(\mathrm{x} 2-\mathrm{x} 0)^*(\mathrm{y} 1-\mathrm{y} 0)\left\{\begin{array}{l} >0 \mathrm{\hspace{0.1cm} p} 2 \text { is on the left side of the line } \\ =0 \mathrm{\hspace{0.1cm} p} 2 \text { is on the same line } \\ <0 \mathrm{ \hspace{0.1cm}p} 2 \text { is on the right side of the line } \end{array}\right.$$

(Game: heads or tails) Write a program that lets the user guess whether the flip of a coin results in heads or tails. The program randomly generates an integer 0 or 1, which represents head or tail. The program prompts the user to enter a guess, and reports whether the guess is correct or incorrect

Use the methods in the following program to print 100 uppercase letters and then 100 single digits, printing ten per line.

1   public class RandomCharacter {
2       /** Generate a random character between ch1 and ch2 */
3       public static char getRandomCharacter(char ch1, char ch2) {
4           return (char)(ch1 + Math.random() * (ch2 - ch1 + 1));
5       }
6
7       /** Generate a random lowercase letter */
8       public static char getRandomLowerCaseLetter() {
9           return getRandomCharacter('a', 'z');
10      }
11
12      /** Generate a random uppercase letter */
13      public static char getRandomUpperCaseLetter() {
14          return getRandomCharacter('A', 'Z');
15      }
16
17      /** Generate a random digit character */
18      public static char getRandomDigitCharacter() {
19          return getRandomCharacter('0', '9');
20      }
21
22      /** Generate a random character */
23      public static char getRandomCharacter() {
24          return getRandomCharacter('\u0000', '\uFFFF');
25      }
26  }

Use the methods in RandomCharacter in Listing 6.10 to print 100 uppercase letters and then 100 single digits, printing ten per line.

Write a method with the following header to format the integer with the specified width. public static String format(int number, int width) The method returns a string for the number with one or more prefix 0s. The size of the string is the width. For example, format(34, 4) returns 0034 and format(34, 5) returns 00034. If the number is longer than the width, the method returns the string representation for the number. For example, format(34, 1) returns 34. Write a test program that prompts the user to enter a number and its width and displays a string returned by invoking format(number, width).

A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon is:

$$\text { Area }=\frac{n \times s^2}{4 \times \tan \left(\frac{\pi}{n}\right)}$$

Write a method that returns the area of a regular polygon using the following header:

public static double area(1nt $\mathrm{n}$, double side)

Write a main method that prompts the user to enter the number of sides and the side of a regular polygon and displays its area.

The formula for computing the area of a regular polygon is

$$\text { Area }=\frac{n \times s^2}{4 \times \tan \left(\frac{\pi}{n}\right)}$$

Write a method that returns the area of a regular polygon using the following header: public static double area(int $\mathrm{n}$, double side) Write a main method that prompts the user to enter the number of sides and the side of a regular polygon and displays its area.

The area of a pentagon can be computed using the following formula:

$$\text { Area }=\frac{5 \times s^2}{4 \times \tan \left(\frac{\pi}{5}\right)}$$

Write a method that returns the area of a pentagon using the following header:

public static double area(double side)

Write a main method that prompts the user to enter the side of a pentagon and displays its area.

The area of a pentagon can be computed using the following formula

$$\text { Area }=\frac{5 \times s^2}{4 \times \tan \left(\frac{\pi}{5}\right)}$$

Write a program that prompts the user to enter the side of a pentagon and displays the area.

(Print calendar) Programming Exercise 3.21 uses Zeller’s congruence to calculate the day of the week. Simplify Listing 6.12, PrintCalendar.java, using Zeller’s algorithm to get the start day of the month.

Earlier Programming Exercise uses Zeller’s congruence to calculate the day of the week. Simplify Listing 5.12, PrintCalendar.java, using Zeller’s algorithm to get the start day of the month.

(Current date and time) Invoking System.currentTimeMillis() returns the elapsed time in milliseconds since midnight of January 1, 1970. Write a program that displays the date and time. Here is a sample run:

Current date and time is May 16, 2012 10:34:23

Invoking System.currentTimeMillis() returns the elapsed time in milliseconds since midnight of January 1, 1970. Write a program that displays the date and time. Here is a sample run: Current date and time is May 16, 2012 10:34:23