(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 $4.8 b$. (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:

Key Concepts

Conditional Logic in Programming

Conditional logic involves using if-else statements to execute different actions based on whether specific criteria are met. In the context of determining point containment, conditional statements are used to verify whether the computed distances (or absolute values) are within the allowed ranges, guiding the program to provide the correct output.

Point Containment

The point containment problem involves determining whether a given point lies within a specified geometric boundary. This requires checking if the point's coordinates satisfy the conditions imposed by the region's limits, ensuring it is neither outside nor on the boundaries if exclusion is desired.

Absolute Value and Distance

Using absolute values is important when calculating distances or comparing positions relative to a central point. In the context of a rectangle centered at the origin, the absolute value of a coordinate gives the linear distance from the center along that axis, which is then compared to half of the rectangle's dimension to determine inclusion.

Coordinate System

A coordinate system provides a framework for representing points in space using numerical values. In a Cartesian coordinate system, each point is defined by an ordered pair (or tuple in higher dimensions), which allows for precise quantitative analysis and geometric computations.

Rectangular Region

A rectangular region in geometry is defined by its boundaries along the horizontal and vertical axes. When centered at a point (often the origin), its dimensions can be described using its width and height, from which the boundaries are derived by taking half the dimensions on each side.

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