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Chapter 3: Problem 22

Plot each point in a rectangular coordinate system. $$ (3,-3) $$

Short Answer

Expert verified
Plot the point (3, -3) by moving 3 units right and 3 units down from the origin.

Step by step solution

01

Understand the coordinates

The given point is represented as \(3, -3\). This means that the x-coordinate is 3 and the y-coordinate is -3.
02

Identify the x-axis

Locate the x-axis on the rectangular coordinate system. This is the horizontal line.
03

Identify the y-axis

Locate the y-axis on the rectangular coordinate system. This is the vertical line.
04

Move along the x-axis

Starting from the origin (0, 0), move 3 units to the right along the x-axis.
05

Move along the y-axis

From the point (3, 0), move 3 units downwards along the y-axis because the y-coordinate is -3. This takes you to the point (3, -3).
06

Plot the point

Mark the point (3, -3) 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
A rectangular coordinate system, also known as the Cartesian coordinate system, is a two-dimensional plane formed by two perpendicular lines: the x-axis and the y-axis. These axes intersect at a point called the origin, which has coordinates (0, 0). The plane is divided into four quadrants, each representing different signs of x and y coordinates.
Using a rectangular coordinate system allows us to precisely locate points using pairs of numbers called coordinates. This system is widely used in mathematics, engineering, physics, and computer graphics.
x-axis
The x-axis is the horizontal line in the rectangular coordinate system. It extends infinitely in both positive and negative directions. The center of the x-axis corresponds to the origin, marked as 0.
Points to the right of the origin have positive x-coordinates, while points to the left have negative x-coordinates. For instance, the point (3, 0) is 3 units to the right of the origin.
The x-axis helps us to find the horizontal position of any point on the plane.
y-axis
The y-axis is the vertical line in the rectangular coordinate system. It also extends infinitely in both positive and negative directions from the origin.
Above the origin, points have positive y-coordinates, while points below the origin have negative y-coordinates. For example, the point (0, -3) is 3 units below the origin.
The y-axis allows us to determine the vertical position of any point on the plane.
coordinates
Coordinates are pairs of numbers that describe the position of a point on the rectangular coordinate system. A coordinate pair is written as (x, y), where x represents the horizontal position and y represents the vertical position.
For example, in the given point (3, -3), '3' is the x-coordinate and '-3' is the y-coordinate. This tells us to move 3 units right from the origin along the x-axis and then 3 units down along the y-axis.
With coordinates, we can uniquely identify any point on the plane, ensuring accurate plotting and navigation.

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