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Chapter 3: Problem 12

plot the given point in a rectangular coordinate system. $$(-5,0)$$

Short Answer

Expert verified
The point (-5,0) is plotted 5 units left from the origin on the x-axis.

Step by step solution

01

Understand Rectangular Coordinate System

A rectangular coordinate system is a two-dimensional number line where the horizontal line is called x-axis and the vertical line is called y-axis. The point where both these axes intersect is called the origin, denoted by (0,0). The value of any point in the rectangular system is given as an ordered pair (x, y).
02

Identify Point Coordinates

The point given is (-5,0). Here, -5 is the x-coordinate and 0 is the y-coordinate. The x-coordinate is negative which means we move to the left from the origin. The y-coordinate is 0 which means we don't move up or down from the x-axis.
03

Plotting the Point in the Coordinate System

Starting from the origin, move 5 units left along the x-axis, this is because the x-coordinate is -5. As the y-coordinate is 0, there is no need to move the point up or down. Mark the point as (-5,0).

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Key Concepts

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

x-axis
In a rectangular coordinate system, the x-axis is the horizontal line that runs left to right. This axis serves as the horizontal reference point for positioning coordinates. It's important to know that the x-axis represents the first number in any coordinate pair, commonly referred to as the x-coordinate.

  • The x-value tells how far to move horizontally.
  • A positive x-coordinate means you move to the right from the origin.
  • A negative x-coordinate means you move to the left along the x-axis from the origin.
Understanding how to use the x-axis effectively can help you accurately plot and interpret points in the rectangular coordinate system. This system is fundamental in making connections between geometry and algebra.
y-axis
The y-axis is the vertical counterpart to the x-axis in the rectangular coordinate system. It runs up and down and intersects with the x-axis at the origin. Just like the x-axis, the y-axis helps to determine the position of points using the second number in the coordinate pair, called the y-coordinate.

  • The y-value tells how far to move vertically.
  • A positive y-coordinate means you move upwards from the origin.
  • A negative y-coordinate means you move downwards along the y-axis from the origin.
The concept of the y-axis is crucial for understanding spatial relationships vertically. When used together with the x-axis, it allows for precise positioning within the plane.
origin
In the rectangular coordinate system, the origin is the point where the x-axis and y-axis intersect. The coordinates of the origin are (0, 0), which makes it the central reference point for the entire system.

  • Starting point: The origin serves as the starting point for plotting any point in the system.
  • Coordinates at the origin are always (0,0).
  • It's a neutral point; neither positive nor negative for x and y coordinates.
Understanding the role of the origin is important because all movements from this point along the x-axis and y-axis form the basis for locating points within the coordinate plane.

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Most popular questions from this chapter

Solve for \(y\) and put the equation in slope-intercept form. $$y-3=4(x+1)$$

Will help you prepare for the material covered in the first section of the next chapter. Is \((4,-1)\) a solution of both \(x+2 y=2\) and \(x-2 y=6 ?\)

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of any equation in the form \(y=m x+b\) passes through the point \((0, b)\)

Will help you prepare for the material covered in the first section of the next chapter. Determine the point of intersection of the graphs of \(2 x+3 y=6\) and \(2 x+y=-2\) by graphing both equations in the same rectangular coordinate system.

What is the graph of an equation?
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