In Exercises 1-12, plot the given point in a rectangular coordinate system. (7/2, - 3/2)

Verified step by step guidance

1. Step 1: Identify the given point in the form (x, y), which is \( \left( \frac{7}{2}, -\frac{3}{2} \right) \).
2. Step 2: Understand that the first value, \( \frac{7}{2} \), represents the x-coordinate, and the second value, \( -\frac{3}{2} \), represents the y-coordinate.
3. Step 3: On a rectangular coordinate system, locate the x-axis and y-axis. The x-axis is horizontal, and the y-axis is vertical.
4. Step 4: Move along the x-axis to the right by \( \frac{7}{2} \) units, since the x-coordinate is positive.
5. Step 5: From the point on the x-axis, move vertically downwards by \( \frac{3}{2} \) units, since the y-coordinate is negative, and plot the point.

Key Concepts

Rectangular Coordinate System

A rectangular coordinate system, also known as the Cartesian coordinate system, consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point in this system is defined by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. This system allows for the precise plotting of points and the visualization of geometric shapes.

Ordered Pairs

An ordered pair is a pair of numbers used to represent a point in a coordinate system. The first number corresponds to the x-coordinate, which indicates the horizontal distance from the origin, while the second number corresponds to the y-coordinate, indicating the vertical distance. For example, the point (7/2, -3/2) means moving 3.5 units to the right and 1.5 units down from the origin.

Plotting Points

Plotting points involves marking a specific location on a coordinate grid based on its ordered pair. To plot the point (7/2, -3/2), one would first locate 3.5 on the x-axis and then move down to -1.5 on the y-axis. This process visually represents the relationship between the two coordinates and is fundamental in graphing functions and analyzing geometric figures.