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Chapter 4: Problem 4

Plot the points on a rectangular coordinate system. $$ (-6,4),(0,0),(3,-2) $$

Short Answer

Expert verified
The points have been plotted successfully at (-6,4), (0,0), and (3,-2) on the rectangular coordinate system.

Step by step solution

01

Recognize Coordinate Pairs

Each pair of numbers provided in parentheses represents a point on a 2-dimensional grid. The first number in the pair, the x-coordinate, tells us how far left or right to go from the origin (0,0). The second number, the y-coordinate, tells us how far up or down to go. Negative x-coordinates indicate positions to the left of the origin, positive to the right. Similarly, negative y-coordinates indicate positions below the origin, positive ones above.
02

Plotting the Point (-6,4)

For the point (-6,4), start at the origin. Move 6 units to the left because the x-coordinate is -6, then move 4 units upwards because the y-coordinate is 4. Put a dot at this location.
03

Plotting the Point (0,0)

For the point (0,0), it means there is no movement either in the x or the y direction. Therefore, put a dot at the origin.
04

Plotting the Point (3,-2)

For the point (3,-2), start at the origin. Move 3 units to the right because the x-coordinate is 3, then move 2 units downwards because the y-coordinate is -2. Put a dot at this location.

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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 plane, is a two-dimensional grid used to locate points using pairs of numbers. These number pairs are known as coordinates. The grid consists of two perpendicular lines:
  • The horizontal line is called the x-axis.
  • The vertical line is called the y-axis.
Where these two axes meet is called the origin, marked as (0,0). Each point in the plane is defined by its distance from the x-axis and the y-axis, allowing us to place points anywhere on the grid by using a combination of positive and negative coordinates. This system is fundamental for graphing relationships and solving geometric problems.
Plotting Points
Plotting points on a rectangular coordinate system means marking specific locations on the grid using coordinates. It is like following a map where each point is determined by two values: its x-coordinate and y-coordinate. To plot a point:
  • Start at the origin, (0,0), which is where the x and y axes intersect.
  • Use the x-coordinate to move left or right.
  • Use the y-coordinate to move up or down.
This method helps visually represent mathematical relationships and is essential for understanding graph-based problems.
X-coordinate
The x-coordinate is the first number in a coordinate pair. It tells us how far to move horizontally from the origin.
  • If the x-coordinate is positive, we move to the right along the x-axis.
  • If it's negative, we move to the left.
In the example exercise, for the point (-6,4), the x-coordinate is -6, which means starting at the origin and moving 6 units to the left. Understanding x-coordinates is crucial as it forms the basis of positioning horizontally on the x-axis.
Y-coordinate
The y-coordinate is the second number in a coordinate pair and it tells us how far to move vertically from the origin.
  • When the y-coordinate is positive, move upwards along the y-axis.
  • If it's negative, move downwards.
In the given point (3,-2), the y-coordinate is -2, indicating we move down 2 units from the x-position. Understanding y-coordinates is essential for accurate vertical positioning and combining it with x-coordinates allows us to find precise locations on the Cartesian plane.

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