Coordinate Plane

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 Meaning

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.

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 in a Coordinate Plane

Signs of coordinates in different quadrants are:

Quadrant	x Coordinate Sign	y Coordinate Sign
I	Positive	Positive
II	Negative	Positive
III	Negative	Negative
IV	Positive	Negative

How to Plot a Point on the 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.

Graph in Coordinate Plane

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.

People Also Read:

• Coordinate Geometry
• Quadrants
• Area of Quadrant
• Distance Between Two Points Formula
• 3D Distance Formula

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.

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.

FAQs on Coordinate Plane

What is a coordinate plane?

A coordinate plane is a visual tool that looks like a grid, with points identified using two numbers: an x-coordinate (horizontal) and a y-coordinate (vertical).

What are some characteristics of a coordinate plane?

Its properties include the ability to label integer numbers, create graphs, visualise mathematical connections, and calculate Cartesian coordinates.

What is the definition of quadrants on a coordinate plane?

Quadrants split the plane into four zones, each with its own set of properties determined by the signs of the coordinates.

What are the signs and symbols that go with quadrants?

Signs and symbols aid in determining the signs of coordinates in each quadrant by expressing the direction and magnitude of vectors, angles, and geometric characteristics.

How do I plot a point on the coordinate plane?

Points are plotted using x and y coordinates to make ordered pairs. Begin by moving horizontally using the x coordinate, then vertically using the y coordinate.

How should I draw a graph on a coordinate plane?

Begin by determining the quadrant for each point, and then place the points on the axes accordingly. Finally, link the points to create a graph.

How can I find the quadrant of a given point?

Check the coordinate signs: both positive in Quadrant I, x negative and y positive in Quadrant II, both negative in Quadrant III, and x positive and y negative in Quadrant IV.