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Chapter 3: Problem 21

Plot each group of points. $$ (1,2),(-2,3),(4,-1),(-5,-3),(4,0),(0,-2) $$

Short Answer

Expert verified
Plot each point by moving horizontally to the x position and vertically to the y position.

Step by step solution

01

Understand the Coordinate System

The coordinate system is a grid defined by an x-axis (horizontal) and a y-axis (vertical). Each point on this grid is defined by an ordered pair \(x, y\), where x represents the horizontal position and y represents the vertical position.
02

Identify the Points

The points provided are (1,2), (-2,3), (4,-1), (-5,-3), (4,0), and (0,-2). Each pair represents an (x, y) coordinate.
03

Plot the Points on the Coordinate Plane

For each point, move horizontally to the x-coordinate and then move vertically to the y-coordinate. Mark the point where the x and y coordinates intersect.
04

Example - Plotting (1, 2)

Starting at the origin (0,0), move 1 unit to the right along the x-axis and 2 units up along the y-axis. Mark the point.
05

Plot the Remaining Points

Repeat the steps for each point:- Move 2 units to the left and 3 units up to plot (-2,3).- Move 4 units to the right and 1 unit down to plot (4,-1).- Move 5 units to the left and 3 units down to plot (-5,-3).- Move 4 units to the right and stay on the x-axis to plot (4,0).- Stay on the y-axis and move 2 units down to plot (0,-2).

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Key Concepts

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

coordinate system
The coordinate system is a fundamental concept in mathematics. It creates a grid using two perpendicular lines (or axes) to locate points. The horizontal line is called the x-axis, and the vertical line is the y-axis. These axes intersect at the origin, which is the point (0,0). The coordinate system allows us to plot points and visualize data in a structured way. Each point on this grid is identified by an ordered pair, defined by the x (horizontal) and y (vertical) coordinates. This system is vital for graphing equations, solving geometric problems, and analyzing patterns.
ordered pairs
An ordered pair is a way of representing the position of a point in the coordinate system. It consists of two numbers: the first number is the x-coordinate, and the second is the y-coordinate. Ordered pairs are written in parentheses with a comma separating the two numbers, like this: (x, y). For example, in the pair (4, -1), 4 is the x-coordinate, and -1 is the y-coordinate. This means to find this point on the coordinate plane, you would move 4 units to the right (along the x-axis) and 1 unit down (along the y-axis). Remember, the order matters in ordered pairs: (4, -1) is not the same as (-1, 4).
x-axis and y-axis
The x-axis and y-axis are the two main components of the coordinate system. The x-axis is the horizontal axis that runs left to right. It is used to plot the horizontal position of a point. Positive values are to the right of the origin, and negative values are to the left. The y-axis is the vertical axis that runs up and down. It is used to plot the vertical position of a point. Positive values are above the origin, and negative values are below it. Together, these axes create a grid that helps to locate points accurately in the four quadrants of the coordinate plane.
graphing points
Graphing points on a coordinate plane involves placing points based on their x and y coordinates. To graph a point, start at the origin (0,0).
  • For the x-coordinate, move horizontally: right for positive values and left for negative values.
  • For the y-coordinate, move vertically: up for positive values and down for negative values.
For example, to graph the point (1,2), move 1 unit to the right and 2 units up. Mark the point where this position intersects. Repeat these steps for each point in your list. By plotting all given points, you can visualize the relationship between them and understand their distribution on the plane.

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