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Chapter 3: Problem 15

Plot each point in a rectangular coordinate system. $$ (-3,-2) $$

Short Answer

Expert verified
Plot (-3,-2) by moving 3 units left and 2 units down from the origin.

Step by step solution

01

Understand the Coordinate System

A rectangular coordinate system consists of two perpendicular lines called the x-axis (horizontal) and y-axis (vertical). The point where they intersect is called the origin (0,0). Points are defined by their positions along these axes.
02

Identify Coordinates

The given coordinates are (-3,-2). The first number, -3, represents the x-coordinate, and the second number, -2, represents the y-coordinate.
03

Locate x-Coordinate

From the origin, move 3 units to the left along the x-axis since the x-coordinate is -3.
04

Locate y-Coordinate

From the position at x = -3, move 2 units down along the y-axis since the y-coordinate is -2.
05

Plot the Point

Mark the point where the coordinates meet at (-3, -2) on the graph. This is the required point.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rectangular Coordinate System
To understand the concept of plotting points, you first need to understand the rectangular coordinate system. This system consists of two perpendicular lines. One is horizontal and is called the x-axis. The other is vertical and is called the y-axis. These axes intersect at a point called the origin, which has the coordinates (0,0). Points are positioned based on their distance from the x-axis and y-axis, labeled as (x, y). By understanding this base, it becomes easier to navigate and plot within this coordinate plane.
X-axis and Y-axis
The x-axis and y-axis are the backbone of the rectangular coordinate system. Here鈥檚 how they work:
The x-axis is horizontal and runs left to right. Positive numbers are to the right of the origin, and negative numbers are to the left.
The y-axis is vertical and runs up and down. Positive numbers are above the origin, and negative numbers are below.
Together, these axes divide the plane into four quadrants. This helps in pinpointing the exact location of points. For example, a point with a negative x-coordinate and a negative y-coordinate, like (-3, -2), will be in the third quadrant, both x and y values being negative.
Graphing Points
Graphing points in the coordinate system is straightforward once you grasp the axes. Let鈥檚 plot the point (-3, -2):
  • Start at the origin (0,0).
  • Move 3 units left along the x-axis since the x-coordinate is -3.
  • From that position, move 2 units down along the y-axis since the y-coordinate is -2.
  • Mark this position. This gives you the point (-3, -2).

By practicing, you'll quickly get the hang of it. Remember, each point is defined by how far left/right and up/down you move from the origin.

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