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Chapter 2: Problem 15

Plot each point in a rectangular coordinate system. $$ (2,3) $$

Short Answer

Expert verified
The point (2,3) is plotted by moving 2 units right and 3 units up from the origin.

Step by step solution

01

Understanding the Rectangular Coordinate System

The rectangular coordinate system, also known as the Cartesian coordinate system, consists of two perpendicular axes: the horizontal axis (x-axis) and the vertical axis (y-axis).
02

Identify the Coordinates

Given point: (2,3). Here, 2 is the x-coordinate (horizontal position), and 3 is the y-coordinate (vertical position).
03

Plot the x-coordinate

Move 2 units to the right of the origin (0,0) on the x-axis.
04

Plot the y-coordinate

From the point (2,0), move 3 units up to reach the point (2,3) on the y-axis.
05

Place the Point

Mark the point (2,3) on the grid where the coordinates intersect. This is the required location of the point in 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
The rectangular coordinate system is a way to pinpoint exact locations on a plane using two perpendicular lines, called axes. These axes divide the plane into four quadrants.
The horizontal axis is called the x-axis, and the vertical axis is called the y-axis. The point where they intersect is called the origin, marked as (0,0).

This system is also known as the Cartesian coordinate system, named after the mathematician Ren茅 Descartes who created it. By using this system, we can describe every point on the plane with a pair of numbers called coordinates.
x-axis and y-axis
The x-axis and y-axis are essential components of the rectangular coordinate system. They allow us to accurately locate points on a plane. The x-axis runs horizontally (left to right) and the y-axis runs vertically (up and down).

When plotting a point like (2,3):
  • The first number (2) is the x-coordinate, and it shows how far to move right (positive) or left (negative) from the origin, along the x-axis.
  • The second number (3) is the y-coordinate, and it shows how far to move up (positive) or down (negative) from the position on the x-axis, along the y-axis.
Together, these coordinates help us locate any point on the plane by moving along both axes.
Coordinates
Coordinates are pairs of numbers that show a specific location on the rectangular coordinate system. They are written as \(x, y\).

The first number is always the x-coordinate, and it tells you the position along the x-axis. The second number is the y-coordinate, and it determines the position along the y-axis.
For example, the point (2,3) has an x-coordinate of 2 and a y-coordinate of 3. To plot this point:
  • Start at the origin (0,0).
  • Move 2 units to the right along the x-axis.
  • Then move 3 units up along the y-axis.
You'll find the point (2,3) where these movements intersect. Marking points in this way helps us represent data, solve equations, and understand geometric shapes in a more visual manner.

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