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Chapter 1: Problem 2

Graph each ordered pair on a coordinate system. $$D(6,0)$$

Short Answer

Expert verified
The point \(D(6,0)\) is on the x-axis, 6 units right of the origin.

Step by step solution

01

Understanding the Coordinate System

The coordinate system consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point on the coordinate plane is represented by an ordered pair \((x, y)\).
02

Identifying Coordinates

In the ordered pair \(D(6,0)\), the first number \(6\) is the x-coordinate (horizontal position), and the second number \(0\) is the y-coordinate (vertical position).
03

Locate the X-coordinate

Start at the origin \((0,0)\) on the coordinate plane. Move 6 units to the right along the x-axis, as the x-coordinate is 6.
04

Locate the Y-coordinate

From \((6,0)\) on the x-axis, identify that the y-coordinate is 0. This means you do not move up or down from the x-axis.
05

Plotting the Point

Since the y-coordinate is 0, the point \(D(6,0)\) lies directly on the x-axis at 6 units right from the origin. Plot the point where the path taken for the x-coordinate meets the x-axis, marking it with a dot labeled \(D\).

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Key Concepts

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

x-axis
The x-axis is a fundamental part of the coordinate system. It runs horizontally across the graph. You can think of it as the line where you measure how far to the right or left a point is. When you look at any ordered pair like
  • \((6, 0)\): Here, the "6" is the x-coordinate.
  • The x-coordinate tells us how many steps to move left or right from the origin \((0, 0)\).

For positive x-coordinates, move to the right of the origin. For negative x-coordinates, move to the left.
It's simple: just remember that the x-axis crosses the origin horizontally like a floor we walk upon from left to right.
y-axis
The y-axis complements the x-axis by running vertically on the coordinate plane. This axis helps to determine how high or low a point is positioned. In an ordered pair:
  • \((6, 0)\): The "0" here represents our y-coordinate.
  • We look at the origin \((0, 0)\) and then move vertically.

If the y-coordinate is positive, we step upwards; if it's negative, we go down. Remember: the y-axis slices through the origin vertically, making it like a ladder that points to the sky. In the ordered pair \((6, 0)\), since the y-coordinate is 0, you won't move up or down, meaning it rests right on the x-axis.
ordered pairs
Ordered pairs are key to finding locations on a graph. Composed as \((x, y)\), they indicate precise spots:
  • The first number denotes the x-coordinate (horizontal movement).
  • The second number gives the y-coordinate (vertical movement).

Let's take \((6, 0)\) again. Here, "6" tells you to move six units along the x-axis, and "0" says don鈥檛 move up or down from there.
The power of ordered pairs lies in their ability to clearly describe exactly where a point exists on the plane, combining both horizontal and vertical information in a neat package.

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