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Chapter 4: Problem 40

Graph each ordered pair. $$(0,3)$$

Short Answer

Expert verified
To graph the ordered pair \((0, 3)\), start at the origin \((0, 0)\) and do not move horizontally since the x-coordinate is 0. Move 3 units up along the y-axis, as the y-coordinate is 3, and plot the point at this location. This point represents the ordered pair \((0, 3)\) on the coordinate plane.

Step by step solution

01

Understand the coordinate plane

A coordinate plane, also known as the Cartesian plane, is a 2D plane formed by two perpendicular number lines called axes - the x-axis (horizontal line) and the y-axis (vertical line). These axes intersect at a point called the origin, which has the coordinates (0, 0). Points on the plane are represented by ordered pairs of numbers (x, y), where 'x' is the distance along the x-axis and 'y' is the distance along the y-axis.
02

Determine the x and y coordinates of the ordered pair

The given ordered pair is (0, 3), which means the x-coordinate is 0 and the y-coordinate is 3. These coordinates tell us how far to move horizontally (left or right from the origin) and vertically (up or down from the origin) to reach our point.
03

Plot the point on the coordinate plane

Start at the origin (0, 0). Since the x-coordinate is 0, we do not move horizontally. Now, move 3 units up vertically, as the y-coordinate is 3. Plot a point at this location. This point represents the ordered pair (0, 3) on the coordinate plane. The point (0, 3) has been successfully graphed on the coordinate plane.

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Key Concepts

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

Coordinate Plane
A coordinate plane, or the Cartesian plane, is a two-dimensional surface marked by two perpendicular lines called axes. These two lines are given special names: the x-axis and the y-axis. The purpose of the coordinate plane is to help us plot points using ordered pairs. Each point on this plane can be defined precisely by a pair of numbers, commonly referred to as coordinates. The coordinate plane is crucial in mathematics as it helps visualize data, solve equations, and understand geometric concepts. This system also aids in graphically representing relationships between variables.

  • The plane is divided into four sections, known as quadrants. Each quadrant helps in placing figures and graphing equations.
  • The coordinate plane helps in understanding and solving real-world problems through graphical representations.
X-axis
The x-axis is the horizontal line on the coordinate plane. It serves as a reference for determining the horizontal position of points. When graphing, the first number in an ordered pair indicates how far along the x-axis you should move starting from the origin. In simpler terms, it tells you how far left or right a point is from the center of the coordinate system.
The x-axis can have both positive and negative values.
  • Positive x-coordinates are located to the right of the origin.
  • Negative x-coordinates are found to the left.
Understanding the x-axis is vital in graphing and interpreting data as it allows one to identify locations and movements horizontally across a graph.
Y-axis
The y-axis is the vertical line on the coordinate plane. It's used to determine the vertical position of a point. In an ordered pair, the second number tells us how far to move along the y-axis from the origin. The y-axis enables us to understand the vertical placement of a point, which is very useful in charting data.
Just like the x-axis, the y-axis has both positive and negative sections.
  • Points with positive y-coordinates are located above the origin.
  • Negative y-coordinates are below the origin.
This understanding is essential for graphing, as it helps visualize how high or low a point is situated on the plane.
Origin
The origin is a special point on the coordinate plane where the x-axis and y-axis intersect. It is the starting point for plotting points and has the coordinates (0, 0). The origin acts as a reference point, so whenever you plot a position, you begin from the origin and move accordingly along the x and y axes.
The origin serves a crucial purpose because:
  • It helps in dividing the plane into four quadrants, helping to locate points better.
  • All movements on the plane are measured from this point, making it central to graphing accurately.
  • Understanding the origin is vital as it is the baseline from which all coordinates are measured.
Without the origin, it would be challenging to have a universally agreed-upon reference point on the coordinate plane.

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Most popular questions from this chapter

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