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Magazine Chapter 9: Problem 2
Plot the points corresponding to the ordered pairs \(A(2,5), B(3,-1)\) \(C(-4,1), D(-2,0), E(4,0), F(-2,-2), G(0,0),\) and \(H(0,-5)\)
Short Answer
Expert verified
Points A to H are plotted in the Cartesian plane based on their coordinates.
Step by step solution
01
Understand the Coordinate System
Visualize the Cartesian plane, which consists of the x-axis (horizontal) and the y-axis (vertical). Positive values are to the right and above the origin (0,0), and negative values are to the left and below the origin.
02
Plot Point A (2, 5)
Locate the x-coordinate (2) on the x-axis and move vertically to the y-coordinate (5). Place a point at the intersection, labeling it as A.
03
Plot Point B (3, -1)
Locate the x-coordinate (3) on the x-axis and move vertically to the y-coordinate (-1). Place a point at the intersection, labeling it as B.
04
Plot Point C (-4, 1)
Locate the x-coordinate (-4) on the x-axis and move vertically to the y-coordinate (1). Place a point at the intersection, labeling it as C.
05
Plot Point D (-2, 0)
Locate the x-coordinate (-2) on the x-axis. Since the y-coordinate is 0, the point lies directly on the x-axis. Place a point at the intersection, labeling it as D.
06
Plot Point E (4, 0)
Locate the x-coordinate (4) on the x-axis. Since the y-coordinate is 0, the point lies directly on the x-axis. Place a point at the intersection, labeling it as E.
07
Plot Point F (-2, -2)
Locate the x-coordinate (-2) on the x-axis and move vertically to the y-coordinate (-2). Place a point at the intersection, labeling it as F.
08
Plot Point G (0, 0)
The coordinates (0, 0) are at the origin. Place a point at this location and label it as G.
09
Plot Point H (0, -5)
Locate the x-coordinate (0) on the x-axis and move vertically to the y-coordinate (-5). Place a point at the intersection, labeling it as H.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Coordinate System
The coordinate system, also known as the Cartesian plane, is a method used to uniquely locate points on a two-dimensional plane using ordered pairs. A coordinate system consists of the following elements:
- The Origin: The point \((0,0)\) where the x-axis and y-axis intersect.
- X-axis: The horizontal axis, representing the set of all real numbers.
- Y-axis: The vertical axis, also representing the set of all real numbers.
- Quadrant I: Both x and y coordinates are positive.
- Quadrant II: The x-coordinate is negative, y-coordinate is positive.
- Quadrant III: Both x and y coordinates are negative.
- Quadrant IV: The x-coordinate is positive, y-coordinate is negative.
Ordered Pairs
Ordered pairs are a fundamental concept in the coordinate system. An ordered pair is written in the form \( (x, y) \) where:
1. Locate the x-coordinate on the x-axis.
2. From this point, move vertically to the y-coordinate.
The intersection of these values is the location of the point on the plane. Each ordered pair corresponds to a unique point in the coordinate system.
- x-coordinate (abscissa): Represents the horizontal position.
- y-coordinate (ordinate): Represents the vertical position.
1. Locate the x-coordinate on the x-axis.
2. From this point, move vertically to the y-coordinate.
The intersection of these values is the location of the point on the plane. Each ordered pair corresponds to a unique point in the coordinate system.
Cartesian Plane
The Cartesian plane is the two-dimensional coordinate system formed by the x-axis and y-axis.
This system, named after Ren茅 Descartes, uses perpendicular lines to create a grid that enables precise point plotting.
On this plane:
This system, named after Ren茅 Descartes, uses perpendicular lines to create a grid that enables precise point plotting.
On this plane:
- Points to the right of the origin have positive x-values, and those to the left have negative x-values.
- Points above the origin have positive y-values, and those below have negative y-values.
- Locate points using ordered pairs.
- Visualize mathematical functions and relationships.
- Understand geometric concepts such as slopes and distances between points.
