Coordinate Plane, also known as the Cartesian plane, is a two-dimensional plane formed by the intersection of two perpendicular number lines, typically referred to as the x-axis and y-axis. Coordinate Plane serves as a graphical representation of ordered pairs of numbers and is widely used in mathematics, particularly in geometry and algebra.
In this article, we will discuss the Coordinate Plane in detail, including origin, axes, quadrants, and coordinates.
What is a Coordinate Plane?
The coordinate Plane resembles a large sheet of graph paper. It consists of two perpendicular lines, one horizontal (the x-axis) and one vertical (the y-axis). These lines meet at the origin, which is commonly labeled (0,0).
Coordinate Plane Definition
The coordinate plane, also known as the Cartesian plane, is a two-dimensional surface defined by a pair of perpendicular axes: the horizontal axis (x-axis) and the vertical axis (y-axis).
Each point on the plane represents a pair of integers known as coordinates. The x-coordinate indicates how far to travel horizontally from the origin (right if positive, left if negative), while the y-coordinate indicates how far to move vertically (up if positive, downward if negative).
There are various parts of any Coordinate Plane i.e.
- Axes
- Origin
- Quadrants
- Coordinates
Let's discuss these parts in detail.
Axes and Origin of Coordinate Plane
In a coordinate plane, the axes are two lines that cross at the origin. Here's the breakdown:
- X-axis: A horizontal line on the plane. It denotes the initial coordinate in an ordered pair (x,y). The x-axis values rise from left to right. Positive values are to the right of the origin, whereas negative values are to the left.
- Y-axis: A vertical line on the plane. It refers to the second coordinate in an ordered pair (x, y). The numbers on the y-axis rise from below to above. Positive values are above the origin, whereas negative ones are below.
- Origin: The origin is the place where the x and y axes cross. It is commonly abbreviated as (0, 0) since its coordinates are zero.
Coordinate Plane Quadrants
Quadrants are two number lines that split the coordinate plane into four areas. Each quadrant has distinct features and is represented by Roman numbers.
- Quadrant I: Quadrant I is located in the upper right, Quadrant I has positive values on both the x and y-axis.
- Quadrant II: Quadrant II is located in the upper left, has negative numbers on the x-axis and positive numbers on the y-axis.
- Quadrant III: Quadrant III is located at the bottom left, Quadrant III has negative values on both the x- and y-axis.
- Quadrant IV: Quadrant IV is located in the bottom right corner, Quadrant IV has positive numbers on the x-axis and negative values on the y-axis.
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Coordinate Plane - x and y axis
In mathematics, coordinates are pairs of integers used to identify points on a graph or grid. Every point in the coordinate plane corresponds to a unique ordered pair of numbers (x, y), where x represents the distance along the x-axis and y represents the distance along the y-axis.
- Abscissa: The abscissa of a point in the Cartesian coordinate system is its x-coordinate.
- Ordinate: The ordinate of a point is its y-coordinate.
For example, the coordinates (3, 5) indicate 3 units to the right and 5 units up from the origin.
Characteristics of a Coordinate Plane
There are various characteristics of coordinate plane such as:
- The coordinate plane is made up of two perpendicular axes termed the coordinate axes, which intersect at a point known as the origin.
- A point's Cartesian coordinates may be calculated by measuring its distance from the origin along the x and y axes.
- The coordinate plane exhibits various types of symmetry, such as reflection symmetry across the x-axis, y-axis, or origin, depending on the nature of the geometric figure or function being analyzed.
Signs in Different Quadrants on a Coordinate Plane
Signs of coordinates in different quadrants are:
Quadrants on a Coordinate Plane |
|---|
| Quadrant | x Coordinate Sign | y Coordinate Sign |
|---|
| I | Positive | Positive |
| II | Negative | Positive |
| III | Negative | Negative |
| IV | Positive | Negative |
Plotting Points on a Coordinate Plane
To determine where a point is on a graph, we utilize x- and y-coordinates.
For example, consider (7,9). Here, the x-coordinate is 7 and the y-coordinate is 9. When plotting this on a graph, we always begin with the x coordinate.
Consider it like delivering directions. The x-coordinate informs us how far we walk horizontally, whereas the y-coordinate tells us how far we travel vertically.
So, for (7,9), we'd shift 7 units to the right first, followed by 9 units up. That is where our point would appear on the graph.
Coordinate Plane Graph
Creating a graph on a coordinate plane involves plotting points, lines, or curves based on mathematical equations or functions, and then connecting these points appropriately. Here's a simplified guide on how to graph in a coordinate plane:
How to locate a Graph in a Coordinate Plane?
Let us learn how to build a graph step by step using the following points: (2, -6), (2,2), and (-4, 3).
- Each point contains a quadrant. (-2,6) is in Quadrant II, (2,2) is in Quadrant I, and (8,-3) is in Quadrant IV.
- Check out the x and y axes. For (-2,6), move 2 units to the left on the x-axis and 6 units up on the y-axis. For (2,2), move 2 units right on the x-axis and 2 unit up on the y-axis. For (-4, 3), move 4 units left on the x-axis and 3 units up on the y-axis.
- Connect each point with a straight line when you've determined where it goes. Take a look at the image for an example.
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Conclusion - Coordinate Plane
In conclusion, the coordinate plane, also known as the Cartesian plane, is a fundamental tool in mathematics for representing and analyzing geometric figures, equations, and functions. It consists of two perpendicular number lines called the x-axis and y-axis, intersecting at the origin (0, 0).
Coordinate Plane Examples
Example 1: Plot the following points on a Coordinate plane:
A (-4, 2), B (4, 4), C (5, -2), D (5, 2)
Solution:
In this we have create a Coordinate plane with this points A (-4, 2), B (4, 4), C (5, -2), D (5, 2). Here A is come in second quadrant, B and D is come in first quadrant and C is in IV quadrant.
Example 2: Here are some points plotted on a coordinate plane. A (3,4), B (-3, 2), C (-4, 4), D (5, -3), E (-2, -2). Look at the points on the graph below and answer the following questions:
a) Which quadrants contain the points C, D, and E?
b) Which points are in either the first or fourth quadrant?
Solution:
In this we have create a Coordinate plane with this points A (3,4), B (-3, 2), C (-4, 4), D (5, -3), E (-2, -2). Here A is come in first quadrant, C and B is come in second quadrant, E is come in III quadrant and D is come in IV quadrant.
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a) C is come in second quadrant, E is come in III quadrant and D is come in IV quadrant.
b) Here A is come in first quadrant and D is come in IV quadrant.
Coordinate Plane Worksheet
Problem 1: Consider the coordinate positions A(-3, 5), B(2, -4), and C(0, 0).
- In which quadrant is point A located?
- What are the indications of the x and y coordinates at point B?
- Determine the coordinates of the origin (point C).
- Graph points A, B, and C on a coordinate plane.
Problem 2: Consider a graph containing the points D(4, 3), E(-2, 5), and F(0, -7).
- Determine which quadrant contains point D.
- What are the indications of the x and y coordinates at point E?
- Determine the coordinates of the origin, point F.
- Place points D, E, and F on a coordinate plane.
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