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Chapter 3: Problem 54

Plot and label each point in a rectangular coordinate system. $$ (5,-4.25) $$

Short Answer

Expert verified
Move 5 units right and 4.25 units down from the origin; plot and label this point.

Step by step solution

01

Understand the coordinates

The point (5, -4.25) consists of two values: the first value (5) is the x-coordinate, and the second value (-4.25) is the y-coordinate.
02

Draw the coordinate axes

Draw a horizontal line (x-axis) and a vertical line (y-axis) intersecting at the origin (0,0).
03

Locate the x-coordinate

From the origin, move 5 units to the right along the x-axis. This is because the x-coordinate is 5.
04

Locate the y-coordinate

From the point (5,0), move 4.25 units down because the y-coordinate is -4.25.
05

Plot and label the point

The point where you end up after moving 5 units to the right and 4.25 units down is (5, -4.25). Plot this point and label it as (5, -4.25).

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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 method to uniquely determine each point in a plane through numerical coordinates. These coordinates are ordered pairs \(x, y\) where:
  • The first number, x, is the x-coordinate, which tells us how far to move horizontally from the origin, or the point (0,0).
  • The second number, y, is the y-coordinate, which tells us how far to move vertically.
This system is incredibly useful in various fields such as mathematics and engineering. To plot points, we use two perpendicular lines known as the coordinate axes.
X-Coordinate
The x-coordinate is the first number in an ordered pair \(x, y\). It specifies the horizontal position of a point in the rectangular coordinate system. A positive x-coordinate indicates a movement to the right of the origin, while a negative x-coordinate indicates a movement to the left. For example, if we have the point (5, -4.25), the x-coordinate is 5. This means starting from the origin (0,0), we move 5 units to the right along the x-axis.
Y-Coordinate
The y-coordinate is the second number in an ordered pair \(x, y\). This value indicates the vertical position of the point in the rectangular coordinate system. A positive y-coordinate means moving up from the origin, whereas a negative y-coordinate means moving down. For example, in the point (5, -4.25), the y-coordinate is -4.25. This means after moving 5 units to the right, we move 4.25 units down.
Coordinate Axes
The coordinate axes consist of two perpendicular lines: the x-axis (horizontal) and the y-axis (vertical). These lines intersect at a point called the origin (0,0). The x-axis is used to plot x-coordinates, while the y-axis is used for plotting y-coordinates. By combining these two axes, we can plot any point in the plane by moving horizontally and then vertically from the origin. Always begin plotting a point by first moving along the x-axis and then the y-axis.

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Most popular questions from this chapter

Graph each linear equation. \(y=2 x-5\)

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