In Exercises 1-12, plot the given point in a rectangular coordinate system. (- 5/2, 3/2)

Verified step by step guidance

1. Step 1: Understand the rectangular coordinate system, which consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical).
2. Step 2: Identify the coordinates of the point given, which are (-\frac{5}{2}, \frac{3}{2}). The first value is the x-coordinate, and the second value is the y-coordinate.
3. Step 3: Locate the x-coordinate on the x-axis. Since the x-coordinate is -\frac{5}{2}, move 2.5 units to the left of the origin (0,0) on the x-axis.
4. Step 4: Locate the y-coordinate on the y-axis. Since the y-coordinate is \frac{3}{2}, move 1.5 units up from the origin (0,0) on the y-axis.
5. Step 5: Plot the point where the x-coordinate and y-coordinate intersect. This is the point (-\frac{5}{2}, \frac{3}{2}) on the rectangular coordinate system.

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' represents the horizontal position and 'y' represents the vertical position. This system allows for the precise plotting of points and the visualization of geometric shapes.

Ordered Pair

An ordered pair is a pair of numbers used to represent a point in a coordinate system. The first number indicates the position along the x-axis, while the second number indicates the position along the y-axis. For example, the ordered pair (-5/2, 3/2) specifies a point located 2.5 units to the left of the origin and 1.5 units above it, providing a clear method for locating points in a two-dimensional space.

Plotting Points

Plotting points involves marking a point on a coordinate grid based on its ordered pair. To plot the point (-5/2, 3/2), one would move left from the origin along the x-axis to -2.5 and then move up to 1.5 on the y-axis. This process is essential for visualizing data, understanding relationships between variables, and solving geometric problems in algebra.