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Chapter 9: Problem 34

For Exercises \(29-34\), plot the points on the rectangular coordinate system. $$(-4,0)$$

Short Answer

Expert verified
Plot the point at \((-4,0)\).

Step by step solution

01

Identify the coordinates

The given point is \((-4,0)\). Here, \(-4\) is the x-coordinate and \(0\) is the y-coordinate.
02

Locate the x-coordinate

Move \(-4\) units to the left from the origin along the x-axis since the x-coordinate is \(-4\).
03

Locate the y-coordinate

Since the y-coordinate is \(0\), stay on the same horizontal level. There is no need to move up or down.
04

Plot the point

Place a point at the position where \(-4\) on the x-axis intersects with \(0\) on the y-axis. This is the point \((-4,0)\).

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Key Concepts

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

rectangular coordinate system
The rectangular coordinate system, also known as the Cartesian coordinate system, is a two-dimensional plane created by two perpendicular lines called axes. The horizontal axis is known as the x-axis, and the vertical axis is referred to as the y-axis. These axes divide the plane into four regions called quadrants. The point where both axes intersect is known as the origin, denoted by \(0,0\). This system allows us to locate any point in the plane using a pair of numbers called coordinates. The first number in the pair represents the x-coordinate, and the second number represents the y-coordinate.
x-coordinate
The x-coordinate of a point indicates its horizontal position relative to the origin in the rectangular coordinate system. If the x-coordinate is positive, the point lies to the right of the origin. If the x-coordinate is negative, the point lies to the left of the origin. For example, in the given point \(-4,0 \), the x-coordinate is \(-4 \), which tells us to move four units to the left from the origin along the x-axis.
y-coordinate
The y-coordinate of a point indicates its vertical position relative to the origin in the rectangular coordinate system. If the y-coordinate is positive, the point is above the origin. If the y-coordinate is negative, the point is below the origin. For example, in the given point \(-4,0 \), the y-coordinate is \(0 \). This means the point remains on the x-axis and there is no need to move up or down.
graphing
Graphing points on the rectangular coordinate system involves locating their coordinates on the plane and marking them. For instance, to graph the point \(-4,0 \), follow these steps:
  • Identify the coordinates: \(-4 \) for the x-coordinate and \(0 \) for the y-coordinate.
  • Move horizontally to \(-4 \) on the x-axis.
  • Since the y-coordinate is \(0 \), do not move vertically.
  • Place a point where the x-coordinate \(-4 \) intersects the y-coordinate \(0 \).
This point represents \(-4,0 \) on the graph. By understanding and practicing these steps, plotting points becomes second nature.

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