(Geometry: point in a rectangle?) Write a program that...

(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 3.9 b. (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. Enter a point with two coordinates: 22 Point (2.0,2.0) is in the rectangle Enter a point with two coordinates: 64 Point (6.0,4.0) is not in the rectangle

(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 3.9 b. (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.
Enter a point with two coordinates: 22 Point (2.0,2.0) is in the rectangle
Enter a point with two coordinates: 64 Point (6.0,4.0) is not in the rectangle

Key Concepts

Absolute Value in Distance Calculations

The absolute value is used to measure the distance from the center to the point along each axis, regardless of direction. This is crucial for checking if the horizontal distance is less than or equal to half the width and if the vertical distance is less than or equal to half the height, which are the conditions required to determine the point's inclusion in the rectangle.

Boundary Determination Using Inequalities

Determining whether a point lies within a rectangle involves comparing the absolute distances of the point's coordinates from the rectangle's center to half the width (for the x-axis) and half the height (for the y-axis). Inequalities are used to confirm if these distances are within the allowed range, ensuring the point is within the rectangle's limits.

Cartesian Coordinate System

The Cartesian coordinate system defines a two-dimensional plane using perpendicular x and y axes, where each point is represented by an (x, y) pair. This system is foundational for locating points, defining shapes, and understanding relative positions in geometry.

Rectangular Geometry

A rectangle is a quadrilateral with opposite sides of equal length and four right angles. In coordinate geometry, a rectangle can be specified by its center point, width, and height, which allows one to calculate its boundaries along the x-axis and y-axis.

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