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Chapter 2: Problem 21

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

Short Answer

Expert verified
Move 2 units left and 4 units up from the origin.

Step by step solution

01

Understand the Rectangular Coordinate System

A rectangular coordinate system has two axes: the x-axis (horizontal) and the y-axis (vertical). The point where they intersect is called the origin, labeled as (0,0). Points are plotted based on their (x,y) coordinates.
02

Identify the Coordinates

The given point is (-2,4), where -2 is the x-coordinate and 4 is the y-coordinate. The x-coordinate tells you how far to move horizontally from the origin, and the y-coordinate tells you how far to move vertically.
03

Move Horizontally According to the x-coordinate

From the origin, move 2 units to the left along the x-axis because the x-coordinate is -2.
04

Move Vertically According to the y-coordinate

From the new horizontal position, move 4 units up along the y-axis because the y-coordinate is 4.
05

Plot the Point

Mark the point where your final position is. This is the point (-2,4).

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Key Concepts

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

Plotting Points
To plot a point in a rectangular coordinate system, you first need to understand the concept of coordinates, which are written as pairs: (x, y). The 'x' value tells you where to move horizontally, and the 'y' value tells you where to move vertically. Here鈥檚 how to do it step-by-step:

1. Identify your point. For example, let's use (-2, 4).
2. Start at the origin (0,0).
3. Move horizontally to -2 (left because it's negative).
4. From there, move vertically up to 4.
5. Mark the spot where you end up.

This is how you plot points like (-2, 4) effectively!
x-axis and y-axis
The rectangular coordinate system consists of two main lines or axes:

x-axis: This is the horizontal axis. Numbers increase as you move right and decrease as you move left.
y-axis: This is the vertical axis. Numbers increase as you move up and decrease as you move down.

These two axes intersect at the origin, creating four quadrants. Understanding the axes helps you determine where to plot any given point.
Origin and Coordinates
The origin is the starting point where the x-axis and y-axis intersect. It鈥檚 represented as (0,0) in coordinate notation.

Coordinates are pairs of numbers written as (x, y) that show exact positions on the grid. The first number (x) tells you how far to move horizontally from the origin, and the second number (y) tells you how far to move vertically.

For instance, in point (-2,4):
  • The -2 indicates moving 2 units left from the origin
  • The 4 indicates moving 4 units up from that new spot
Coordinates help you precisely locate points in the rectangular coordinate system.

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