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Chapter 3: Problem 48

Plot and label each point in a rectangular coordinate system. $$ (5,3) $$

Short Answer

Expert verified
Plot the point (5,3) by moving 5 right and 3 up; label it as (5,3).

Step by step solution

01

Identify the coordinates

The given point is \(5,3)\). Here, 5 is the x-coordinate, and 3 is the y-coordinate.
02

Draw the rectangular coordinate system

Draw a horizontal axis (x-axis) and a vertical axis (y-axis) that intersect at the origin (0,0).
03

Locate the x-coordinate

Starting at the origin, move 5 units to the right along the x-axis, because the x-coordinate is 5.
04

Locate the y-coordinate

From the point (5,0) on the x-axis, move 3 units up, because the y-coordinate is 3.
05

Plot and label the point

Mark the point where you have moved 5 units right and 3 units up. Label this point as (5,3).

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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, also known as the Cartesian coordinate system, is a way to locate points on a plane using two perpendicular lines called axes. This system divides the plane into four quadrants and allows us to describe the position of any point using a pair of numbers. These numbers are called coordinates. The intersection of these two lines is called the origin and has the coordinates (0,0).
x-axis and y-axis
The x-axis and y-axis are the two main components of the rectangular coordinate system. The x-axis is the horizontal line, while the y-axis is the vertical line. Together, they form a grid that we can use to plot points.
The x-coordinate of a point tells us how far to move right (positive) or left (negative) from the origin along the x-axis. The y-coordinate tells us how far to move up (positive) or down (negative) along the y-axis.
  • For example, in the point (5,3), 5 is the x-coordinate, so we move 5 units to the right along the x-axis.
  • Next, 3 is the y-coordinate, so we move 3 units up along the y-axis.
This way, we can precisely locate the point on the plane.
coordinate plane
A coordinate plane is formed by the intersection of the x-axis and y-axis. It allows us to plot points and show their relationships. The plane is divided into four quadrants:
  • Quadrant I: Both coordinates are positive.
  • Quadrant II: The x-coordinate is negative, and the y-coordinate is positive.
  • Quadrant III: Both coordinates are negative.
  • Quadrant IV: The x-coordinate is positive, and the y-coordinate is negative.
Understanding this helps when plotting points like (5,3), which is in Quadrant I because both coordinates are positive.
By recognizing which quadrant a point belongs to, we can quickly verify if our plotted point is accurate.

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Most popular questions from this chapter

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