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Magazine Chapter 1: Problem 32
Graph each ordered pair on a coordinate system. $$X(5,0)$$
Short Answer
Expert verified
The ordered pair \((5,0)\) is located on the \(x\)-axis, directly at \(x = 5\).
Step by step solution
01
Understand the Ordered Pair
An ordered pair consists of two numbers inside parentheses, usually written in the form \((x, y)\). For the pair \(X(5,0)\), \(x = 5\) and \(y = 0\).
02
Set Up the Coordinate System
A coordinate system consists of two perpendicular lines: the horizontal \(x\)-axis and the vertical \(y\)-axis. Points are located based on their \(x\) and \(y\) values.
03
Locate the x-coordinate
Find the value of \(x = 5\) on the \(x\)-axis, which is the horizontal line. Move right from the origin (0,0) to the location marked 5 on the \(x\)-axis.
04
Locate the y-coordinate
The \(y\)-coordinate is 0, meaning you do not move up or down from the \(x\)-axis. Stay on the \(x\)-axis where \(x = 5\).
05
Plot the Ordered Pair
Where you have located \((x,y)\) by the rules of the previous steps is the point \(X\). It lies directly on the \(x\)-axis at \(x=5\). Draw a dot or mark there to represent the point \((5,0)\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ordered Pair
An ordered pair is a fundamental concept in coordinate geometry. It consists of two elements written in a specific order, usually as \((x, y)\). The first element is always the x-coordinate, and the second is the y-coordinate. Ordered pairs are essential for identifying the position of points on a graph, allowing us to pinpoint exact locations in a two-dimensional space.
- The x-coordinate indicates how far a point is from the vertical y-axis.
- The y-coordinate indicates how far a point is from the horizontal x-axis.
Graphing Points
Graphing points involves placing a point on the coordinate plane at the specific location indicated by an ordered pair. The coordinate plane consists of a grid formed by two perpendicular axes: the x-axis and the y-axis.
To graph a point like \((5, 0)\), follow these simple steps:
To graph a point like \((5, 0)\), follow these simple steps:
- Start at the origin, which is the intersection point of the x-axis and y-axis (0,0).
- Move horizontally to the right to reach the x-coordinate value along the x-axis, which is 5.
- Then, move vertically up or down depending on the y-coordinate value. In this case, stay on the x-axis since the y-coordinate is 0.
- Make a small dot or mark at this location to represent the point.
x-axis and y-axis
The x-axis and y-axis are the two number lines that create the backbone of the coordinate system. These axes intersect at a point called the origin, marked as \((0,0)\). The x-axis runs horizontally and extends infinitely in both left and right directions, while the y-axis runs vertically and extends infinitely upward and downward.
Key aspects to remember:
Key aspects to remember:
- The x-axis is used to determine the horizontal position of a point. Positive numbers lie to the right of the origin, and negative numbers lie to the left.
- The y-axis is used to determine the vertical position of a point. Positive numbers are above the origin, and negative numbers are below.
Plotting Points
Plotting points on a coordinate system involves more than just marking a spot. It requires an understanding of both mathematical concepts and visualizing spatial relationships. When plotting a point like \(X(5,0)\), the x-coordinate tells you how far to move horizontally from the origin, and the y-coordinate tells you how far to move vertically.
Here's a simple way to plot points:
Here's a simple way to plot points:
- Locate the x-coordinate on the x-axis and start moving from the origin along this line.
- Next, check the y-coordinate to determine whether you move up or down. In this example, the y-coordinate is 0, so you remain at your horizontal position.
- Finally, place a dot or mark at this position, confirming the plotted location of the point.
