A coordinate plane is a two-dimensional plane formed by the intersection of a vertical line called the y-axis and a horizontal line called the x-axis. These are perpendicular lines that intersect each other at zero, and this point is called the origin.
|1.||What is a Coordinate Plane?|
|2.||Quadrants on a Coordinate Plane|
|3.||Locating A Point on the Coordinate Plane|
|4.||Plotting A Point on the Coordinate Plane|
|5.||FAQs on Coordinate Plane|
What is a Coordinate Plane?
A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line called the X-axis and a vertical line called the Y-axis intersect at a point called the origin. The numbers on a coordinate grid are used to locate points. A coordinate plane can be used to graph points, lines, and much more. It acts as a map and yields precise directions from one point to another.
Coordinate Plane Definition
The coordinate plane definition is as follows: A coordinate plane, also known as a rectangular coordinate plane grid, is a two-dimensional plane formed by the intersection of a vertical line called the Y-axis and a horizontal line called the X-axis.
Coordinate Plane Graph
Coordinates are a set of two values that locate a specific point on a coordinate plane grid, better known as a coordinate plane. A point in a coordinate plane is named by its ordered pair (x, y), written in parentheses, corresponding to the X-coordinate and the Y-coordinate. These coordinates can be positive, zero, or negative, depending on the location of the point in the respective quadrants.
Quadrants on a Coordinate Plane
A quadrant can be defined as a region/part of a cartesian or coordinate plane obtained when the two axes intersect each other.
- First quadrant: x > 0, y > 0
- Second quadrant: x < 0, y > 0
- Third quadrant: x < 0, y < 0
- Fourth quadrant: x > 0, y < 0
Locating a Point on the Coordinate Plane
Now that we are already familiar with the coordinate plane and its parts, let's discuss how to identify points on a coordinate plane. To locate a point on the coordinate plane, follow the steps given below:
- Step 1: Locate the point.
- Step 2: Find the quadrant by looking at the signs of its X and Y coordinates.
- Step 3: Find the X-coordinate or abscissa of the point by reading the number of units the point is to the right/left of the origin along the X-axis.
- Step 4: Find the Y-coordinate or the ordinate of the point by reading the number of units the point is above/below the origin along the Y-axis.
Let's look at the coordinate plane examples. Look at the figure shown below.
- Step 1: Observe the blue dot on the coordinate graph.
- Step 2: It is in the second quadrant.
- Step 3: The point is 3 units away from the origin along the negative X-axis.
- Step 4: The point is 2 units away from the origin along the positive Y-axis.
Thus, the point on the graph has coordinates (-3, 2).
Plotting a Point in the Coordinate Plane
In this section, we are going to learn how to plot a point on the coordinate plane. Let's take the example of point P = (5, 6). To plot a point in the coordinate plane, follow the steps given below:
- Step 1: Draw two perpendiculars, the X-axis and Y-axis.
- Step 2: Start from the origin. Move 5 units to the right, along the positive X-axis.
- Step 3: Move 6 units up, along the positive Y-axis.
- Step 4: Mark the point of intersection. Mark it as (5, 6).
Note that P is in the first quadrant. Also, this is known as the positive coordinate plane as the value of both the coordinates for any point in this quadrant will be positive.
Important Points on Coordinate Plane:
- The first quadrant (+, +) known as the positive coordinates quadrant, is represented by the Roman numeral I.
- The second quadrant (-, +) is represented by the Roman numeral II.
- The third quadrant (-, -) is represented by the Roman numeral III.
- The fourth quadrant (+, -) is represented by the Roman numeral IV.
- The coordinates of any point are enclosed in brackets.
Try to Solve this Challenging Question:
Find out any three points that lie in the positive coordinate plane and for which the abscissa and ordinate are equal and non-negative.
Topics Related to Coordinate Plane
Examples on Coordinate Plane
Example 1: Let's help Olivia and Jane plot the following points in the Cartesian plane:
A (2.5, 3.5)
B (- 2, 4)
C (6.5, 1)
D (4, - 2.2)
A and C are in the first quadrant.
B is in the second quadrant.
D is in the fourth quadrant.
Example 2: Here are a few points plotted in a coordinate plane:
A (1,2), B ( 3, -2), C (-3, -3), D ( -4, 2), E (-1, 2), F (3,0), G (0, -3)
Look at the points plotted in the graph below and answer the following questions:
a) In which quadrants do the points C, D and, E lie?
b) Which points lie in either the first or the fourth quadrants?
c) Which points lie on one of the two axes?
a) D and E lie in the second quadrant, and C lies in the third quadrant.
b) A lies in the first quadrant, and B lies in the fourth quadrant.
c) F lies on the positive side of the X-axis, and G lies on the negative side of the Y-axis.
Example 3: A person rolls two rolling dice at the same time. Let the numbers which show on Die - 1 and Die - 2 be represented by x and y respectively. After each roll, the point P(x, y) is plotted in the plane. Plot all the possible positions of P, and highlight those positions for which the sum of x and y is 8.
Note that on each die, we can have 6 numbers (integers from 1 to 6). Thus, if you combine the possible numbers from both dice, you have 36 pairs. Now, the pairs for which the sum of x and y is 8 are: (2,6), (3,5), (4,4), (5,3), (6,2). In the following figure, 36 total pairs have been plotted, and these 5 pairs have been highlighted:
FAQs on Coordinate Plane
What is a Coordinate Plane in Geometry?
A coordinate plane is a two-dimensional plane formed by the intersection of the x-axis, the horizontal line, and the y-axis, the vertical line. These perpendicular lines intersect each other at a point called the origin.
Who Invented the Coordinate Plane?
The coordinate system was invented in the 17th century by the French mathematician René Descartes.
What are the Parts of a Coordinate Plane?
Coordinate planes include the axes (X-axis and Y-axis), the origin (0,0), and the four quadrants.
What is Origin on a Coordinate Plane?
The point of intersection of two axes of the coordinate plane is the origin of the coordinate plane. The coordinates of the origin are (0, 0).
What is an XY Coordinate?
The XY-coordinate is a two-dimensional plane with coordinate axes, the X-axis and Y-axis, perpendicular to each other.
How do you Construct a Coordinate Plane?
A coordinate plane can be constructed in the following manner:
- Step 1: Take a sheet of graph or grid paper.
- Step 2: Draw a horizontal line. This line is called the x-axis and is used to locate values of x.
- Step 3: Draw a vertical line. This line is called the y-axis and is used to locate values of y. To show that the axis actually
Note: To show that these axes actually go on forever in both directions, use small arrowheads at each end of the line.
When would you Use a Coordinate Plane?
The Cartesian coordinate plane of x and y works well with so many situations in real life, such as when planning for the placement of different pieces of furniture in a room, a two-dimensional grid can be drawn representing the room and thus an appropriate unit of measurement can be used.
How to Graph on a Coordinate Plane?
Any point or object can be graphed in a coordinate using the coordinates. The coordinates of given points can be plotted in the respective quadrants of the coordinate plane and joined to form the particular shape or object.
How Many Quadrants are there in a Coordinate Plane?
There are four quadrants in a coordinate plane. These four quadrants are represented using Roman numerals I, II, III, and IV, depending upon the signs of the coordinates.
How to Read a Coordinate Plane?
We can read the coordinate plane in the following way:
- Step 1: Find the quadrant in which the given point is located by looking at the signs of its x and y coordinates.
- Step 2: Read the number of units the point is to the right/left of the origin along the x-axis to find its x coordinate.
- Step 3: Read the number of units the point is to the upward/downward side of the origin along the y-axis to find its y coordinate.