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Magazine Chapter 2: Problem 1
Plot the given points in a coordinate plane: $$ (2,3),(-2,3),(4,5),(4,-5),(-4,5),(-4,-5) $$
Short Answer
Expert verified
Plot each point at its designated location based on x and y coordinates.
Step by step solution
01
Understanding the Coordinate Plane
The coordinate plane consists of two axes: the x-axis (horizontal) and the y-axis (vertical). Each point on this plane has two numbers: the first is the x-coordinate and the second is the y-coordinate. The x-coordinate tells how far to move right (positive) or left (negative) from the origin (0,0), and the y-coordinate tells how far to move up (positive) or down (negative).
02
Plotting the Point (2,3)
Start at the origin (0,0). Move 2 units to the right on the x-axis (since 2 is positive), then move 3 units up (since 3 is positive) on the y-axis. Plot the point at this location.
03
Plotting the Point (-2,3)
Begin at the origin. Move 2 units to the left on the x-axis (since -2 is negative), then move 3 units up on the y-axis. Plot the point at this location.
04
Plotting the Point (4,5)
From the origin, move 4 units to the right on the x-axis, and then 5 units up on the y-axis. Mark this point on the plane.
05
Plotting the Point (4,-5)
Begin at the origin. Move 4 units to the right on the x-axis (since 4 is positive), then move 5 units down on the y-axis (since -5 is negative). Plot this point.
06
Plotting the Point (-4,5)
Starting from the origin, move 4 units to the left on the x-axis, and then 5 units up on the y-axis. Plot the point at this position.
07
Plotting the Point (-4,-5)
From the origin, move 4 units to the left on the x-axis, and then 5 units down on the y-axis. Mark this location as the final point.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Cartesian coordinates
A fundamental aspect of mathematics involves understanding Cartesian coordinates.
These coordinates provide a way to determine the position of points in a two-dimensional space, more commonly known as a coordinate plane.
It is named after Ren茅 Descartes, who developed this system as a way to directly link geometry and algebra.
Each point in a Cartesian coordinate system is represented as an ordered pair, like \((x, y)\). Here:
These coordinates provide a way to determine the position of points in a two-dimensional space, more commonly known as a coordinate plane.
It is named after Ren茅 Descartes, who developed this system as a way to directly link geometry and algebra.
Each point in a Cartesian coordinate system is represented as an ordered pair, like \((x, y)\). Here:
- The first number tells you how far to move from the origin along the x-axis (easting).
- The second number tells you how far to move along the y-axis (northing). If a number is negative, it typically means moving in the opposite direction.
x-axis and y-axis
The x-axis and y-axis are two crucial components of the coordinate plane.
The x-axis runs horizontally left to right, while the y-axis runs vertically up and down.
These axes meet at the point \((0,0)\), aptly named the origin.
The x-axis:
The x-axis runs horizontally left to right, while the y-axis runs vertically up and down.
These axes meet at the point \((0,0)\), aptly named the origin.
The x-axis:
- Is the baseline from which you measure horizontal distance.
- Positive numbers lie to the right of the origin, and negative numbers lie to the left.
- Is used to measure vertical distances.
- Positive numbers are marked above the origin, and negative numbers fall below it.
plotting points
Plotting points on a coordinate plane involves using Cartesian coordinates and the x and y axes to place points accurately.
This process begins at the origin, the center point where the x-axis and y-axis intersect.
Here's how to plot a point, like \((2, 3)\):
This process begins at the origin, the center point where the x-axis and y-axis intersect.
Here's how to plot a point, like \((2, 3)\):
- Start at the origin \((0, 0)\).
- Move 2 units right along the x-axis because the x-coordinate is positive.
- Then, move 3 units up because the y-coordinate is also positive.
- Mark the point by drawing a dot.
- Start at the origin.
- Move 4 units left on the x-axis because of the negative x-coordinate.
- Then, move 5 units down due to the negative y-coordinate.
- Place your mark at this spot as the plotted point.
