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Chapter 4: Problem 6

Plot the points on a rectangular coordinate system. $$ (-1,3),(0,2),(-4,-4),(-1,0) $$

Short Answer

Expert verified
The four points (-1,3), (0,2), (-4,-4), and (-1,0) were plotted on the rectangular coordinate system.

Step by step solution

01

Identify the Points

The given points are (-1,3), (0,2), (-4,-4), and (-1,0).
02

Draw the Coordinate Plane

Sketch a coordinate plane, including the x and y axis. The x axis is the horizontal line, while the y axis is vertical. The point where they intersect, or cross, is the origin (0,0).
03

Plot the Points

Begin plotting the points. First, plot (-1,3). Start at the origin, move 1 unit to the left on the x-axis (since -1 is negative), and then move 3 units up (because 3 is positive). Do the same for (0,2); from the origin, do not move along the x-axis (since 0 is on the origin), but move 2 units up. Similarly, plot (-4,-4) by moving 4 units to the left and 4 units down from the origin. Finally, plot (-1,0) by moving to the left by 1 unit and remaining along the x-axis (since y is zero).
04

Specify the Points

Label each point on the graph with its corresponding coordinates.

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Key Concepts

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

Plotting Points
Plotting points on a coordinate plane is a fundamental skill in graphing math problems. Every point is represented by a pair of numbers in parentheses, known as coordinates. The first number in each pair represents the position on the x-axis, and the second number indicates the position on the y-axis. To plot a point, you'll need to follow these simple steps:
  • Identify the coordinates of the point.
  • Find the correct starting position (usually the origin).
  • Move horizontally to the appropriate position based on the x-coordinate.
  • Then, move vertically according to the y-coordinate.
Take the example point (-1, 3): you start from the origin, move 1 step left (because of the negative x value) and then 3 steps up (positive y value). Plotting involves not just placing the point, but also labeling it with its coordinates.
X and Y Axes
The x and y axes form the backbone of the coordinate plane. These two perpendicular lines help us assign a unique location to each point we plot.
  • X-axis: This is the horizontal line. Points on this axis have a y-coordinate of 0.
  • Y-axis: This is the vertical line. If a point is located on this axis, its x-coordinate will be 0.
Together, these axes divide the plane into four quadrants. Moving right from the origin along the x-axis increases the x coordinate, while moving left decreases it. For the y-axis, moving up increases the y coordinate, and moving down decreases it. Understanding these axes is crucial for accurately placing any given point.
Rectangular Coordinate System
The rectangular coordinate system, also known as the Cartesian plane, provides a two-dimensional space for graphing points. This system consists of a grid that is defined by the x-axis and y-axis. Think of it like a graph paper where the intersections of the lines create squares or rectangles:
  • Each point on this system is defined by a pair of coordinates (x, y).
  • These coordinates are distance values that show how far the point is from the origin along the x and y axes.
  • It's a universal system that can be used in various fields, such as mathematics, physics, and engineering.
This system allows for easy visualization of relationships between points, making it essential for tasks such as plot functions or solving equations.
Origin
The origin is a special point on the coordinate plane. It is where the x and y axes intersect, and is represented by the coordinates (0,0).
  • All measurements on the plane start from this point.
  • It serves as a reference point for plotting all other points.
  • Located at the center of the quadrants, it divides them equally.
Every time you plot a new point, you use the origin as your starting location. Therefore, understanding the role of the origin is critical for any graphing activity on the coordinate system. It helps ensure accuracy and consistency across plotting exercises.

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Most popular questions from this chapter

In Exercises 1-4, determine whether each ordered pair is a solution of the inequality. \(-3 x+5 y \leq 12\) (a) \((1,2)\) (b) \((2,-3)\) (c) \((1,3)\) (d) \((2,8)\)

In Exercises \(13-16\), sketch the graph of the linear inequality. $$ y \geq 3 $$

In Exercises 47-52, write the statement as a linear inequality. Then sketch the graph of the inequality. \(y\) is more than six times \(x\).

In Exercises \(37-40\), use the point-slope form to write an equation of the line that passes through the point and has the specified slope. Write the equation in slope-intercept form. $$ \left(0, \frac{3}{2}\right), m=\frac{2}{3} $$

In Exercises 57-60, simplify the expression. $$ x^{2}\left(x y^{3}\right) $$
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