Q:

(Geometry: point in a rectangle?) Write a program that prompts the user to enter a point (x, y) and checks whether the point is within the rectangle centered at (0, 0) with width 10 and height 5

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(Geometry: point in a rectangle?) Write a program that prompts the user to enter a point (x, y) and checks whether the point is within the rectangle centered at (0, 0) with width 10 and height 5.

For example, (2, 2) is inside the rectangle and (6, 4) is outside the rectangle, as shown in Figure 3.7b. (Hint: A point is in the rectangle if its horizontal distance to (0, 0) is less than or equal to 10 / 2 and its
vertical distance to (
0, 0) is less than or equal to 5.0 / 2. Test your program to cover all cases.) Here are two sample runs.

Output:

Enter a point with two coordinates: 2 2
Point (2.0, 2.0) is in the rectangle

Enter a point with two coordinates: 6 4
Point (6.0, 4.0) is not in the rectangle

(b) Points inside and outside of the rectangle.

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/*
(Geometry: point in a rectangle?) Write a program that prompts the user to enter
a point (x, y) and checks whether the point is within the rectangle centered at
(0, 0) with width 10 and height 5. For example, (2, 2) is inside the rectangle and
(6, 4) is outside the rectangle, as shown in Figure 3.7b. (Hint: A point is in the
rectangle if its horizontal distance to (0, 0) is less than or equal to 10 / 2 and its
vertical distance to (0, 0) is less than or equal to 5.0 / 2. Test your program to
cover all cases.) Here are two sample runs.
*/
import java.util.Scanner;

public class Exercise_03_23 {
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);

		// Prompt the user to enter a point (x, y)
		System.out.print("Enter a point with two coordinates: ");
		double x = input.nextDouble();
		double y = input.nextDouble();

		// Check whether the point is within the rectangle
		// centered at (0, 0) with width 10 and height 5
		boolean withinRectangle = (Math.pow(Math.pow(x, 2), 0.5) <= 10 / 2 ) ||
										  (Math.pow(Math.pow(y, 2), 0.5) <= 5.0 / 2);

		// Display results
		System.out.println("Point (" + x + ", " + y + ") is " +
			((withinRectangle) ? "in " : "not in ") + "the rectangle");
	}
}

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