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Chapter 3: Problem 18

Plot each point in a rectangular coordinate system. $$ (-2,-4) $$

Short Answer

Expert verified
Plot at (-2,-4). Move 2 left and 4 down from origin.

Step by step solution

01

- Understand the Coordinates

Coordinates are given in the form \(x, y\), where x represents the horizontal position and y represents the vertical position.
02

- Identify the x-coordinate

The x-coordinate of the point is -2. This means you need to move 2 units to the left from the origin (0,0).
03

- Identify the y-coordinate

The y-coordinate of the point is -4. This means you need to move 4 units down from the origin (0,0).
04

- Plot the Point

Starting from the origin (0,0), move 2 units to the left and then 4 units down. Mark this point on the rectangular coordinate system.

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Key Concepts

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

Rectangular Coordinate System
To understand plotting points, we first need to be familiar with the rectangular coordinate system. This system is also known as the Cartesian coordinate system.
It consists of two perpendicular lines, called axes, which intersect at a point called the origin.
The horizontal axis is called the x-axis and the vertical axis is called the y-axis.
Points in this system are defined by a pair of numbers known as coordinates. Each pair \(x, y\) gives the position of a point where x corresponds to the horizontal position, and y to the vertical position.

In this system:
  • The origin is the point \(0,0\).
  • Moving right from the origin increases the x-coordinate.
  • Moving left decreases it.
  • Moving up from the origin increases the y-coordinate.
  • Moving down decreases it.
X-Coordinate
The x-coordinate is the first number in any point and it tells us how far to move horizontally from the origin. Consider the point \(-2, -4\): Here, -2 is the x-coordinate. This means we will move 2 units to the left of the origin.

Key points about the x-coordinate:
  • If it is positive, move to the right.
  • If it is negative, move to the left.
When plotting the point \(-2, -4\), the x-coordinate requires you to start at the origin and move two units left. The following steps will help assure you move correctly:
  • Start at the origin \(0, 0\).
  • Move left because the x-coordinate is -2.
  • Count 2 units to the left and stop.
This is how you handle the x-coordinate portion of plotting.
Y-Coordinate
The y-coordinate is the second number in any point and it tells us how far to move vertically from the origin. For the point \(-2, -4\), -4 is the y-coordinate. This tells us to move 4 units down from where we stopped after moving left for the x-coordinate.

Key points about the y-coordinate:
  • If it is positive, move up.
  • If it is negative, move down.
To plot the y-coordinate:
  • After moving 2 units to the left (as dictated by the x-coordinate), look at the y-coordinate.
  • Here, it is -4, so move down 4 units.
  • Count these 4 units carefully and stop.
  • Mark this final position to plot the point

Combining both coordinates correctly will place you accurately in the rectangular coordinate system! Plotting correctly means you've applied the concepts of both x and y coordinates properly.

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Most popular questions from this chapter

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