Introduction to Online Graphing Calculator?
The online graphing calculator is a versatile tool that enhances your learning ability and analyzes cartesian coordinates in graphical representation. You just give the equation or points of coordinate planes, and it can easily plot a graph in a few seconds.
It is a helpful tool for everyone, especially for researchers or students who did research work through the mathematical data analysis method, where the coordinate grid process is commonly used to represent plane coordinates into graphs.
What is a Coordinate Grid or Graphing?
A coordinate grid, also named a coordinate plane or cartesian plane, is a two-dimensional plane with a horizontal axis (x-axis) and a vertical axis (y-axis). The intersecting point at which they meet is called the origin.
This system is used to graphically represent plot points, lines, and curves in mathematical data analysis or scientific study.
How to Find Grid Coordinates?
To find the grid coordinates of a point on a coordinate plane, you need to identify the x coordinates on the horizontal plane and the y coordinates on the vertical plane. Here’s a step-by-step guide on how to find the grid coordinates.
If you have the equation, then you can assume one of the coordinate point to find the order pair coordinates for sketching the graph.
Step 1: Identify the point on the coordinate grid for which you want to find the coordinates.
Step 2: Draw the perpendicular lines on the axes in which there is a vertical line on the x-axis. Draw a horizontal line to the y-axis. The central point where both lines intersect is called its origin (0, 0).
Step 3: Now, point out the value of x-coordinate on the x-axis of the graph.
Step 4: Now, point out the value of the y-coordinate on the y-axis of the graph.
Step 5: Lastly, combine the x-coordinate and y-coordinate into an ordered pair (x, y), in which pair coordinates are met with the help of a line on a graph that shows their position.
You can further understand this graphing coordinate concept with the help of our coordinate grid or graph calculator.
Practical Example of Graphing Coordinates:
Let's see some examples of graphing coordinates and their graphical representation.
Example:
On a grid plot point A, having coordinates (-2, 4), point B with coordinates (3,-2), and point C with coordinates (-4, -3).
Solution:
PASTE THE GRAPH HERE!
For straight lines:
Draw the graph of y = 2x -1.
Solution:
The possible point is given as an x-value,
$$ (4, ?),\; (2, ?),\; (-2, ?) $$
Now calculate the y-values using y = 2x - 1,
For the first point x = 4, so
$$ y \;=\; 2 \times 4 - 1 $$
$$ =\; 7 $$
The coordinates of these points are (4,7).
For the second point x = 2, so
$$ y \;=\; 2 \times 2 - 1 $$
$$ =\; 3 $$
The coordinates of the second point are (2,3).
For the third point is (-2, -5).
The graph of a straight line using these points is:
PASTE THE GRAPH HERE!
How to Use Graph Calculator?
The graphic calculator has a user-friendly design that enables you to find the cartesian coordinates for graph. Before adding the input of coordinate graphing problems, you need to follow our given instructions.
- Enter the particular equation in the input box to find the coordinate graphing questions.
- Recheck your input equation before hitting the calculate button of graph solver online to start the calculation process.
- Click on the “Calculate” button to get the result for your given coordinate graphing problems.
- If you want to try our graphing display calculator online for the first time, then you can use the load example option.
- Click on the “Recalculate” button to get a new page for solving more graphing coordinate problems.
Results from 3d Graphing Calculator:
The graphing solver online gives you the solution for the problem when you give it an input. It provides you solutions that includes as:
When you click on the result option, it provides you the result in the form of a graph as per your given equation.
When you click on the possible steps option, it gives you step by step solution to coordinate grid problems.
If you click on this option, it will provide a graph based on the input value you provide to help you visually understand the data.
Advantages of Graphic Calculator:
The graphing tool has many advantages that you can use whenever you plot a graph from an equation in solutions. These advantages are:
- Our calculator graphing is a manageable tool that can sketch graphs from various equations of coordinate geometry.
- With the help of internet, you can use this free graphing display calculator online to find solution of coordinate plane.
- Our tool saves the time and effort you consume in sketching graphs and calculate the equation in cartesian points.
- It is a learning tool, so you can this graph solver online for practicing this concept thoroughly.
- The graphing solver online is a trustworthy tool that provides accurate solutions according to your carestain plane input.
- Our 3d graphing calculator provides a solution in the form of a graph in which the carestain points are well pointed.
Find the coordinates of given equation and draw a graph.
Complete the table below using the relationship, y = x2 - 2
Solution:
For each value of x and y , lets use the given equation
$$ y \;=\; x^{2-2} $$
$$ \begin{matrix} x \;=\; 3 & x \;=\; 2 & x \;=\; 1 & x \;=\; 0 \\ y \;=\; (3)^{2-2} & y \;=\; (2)^{2-2} & y \;=\; (1)^{2-2} & y \;=\; (0)^{2-2} \\ y \;=\; 9 - 2 & y \;=\; 4 - 2 & y \;=\; 1 - 2 & y \;=\; 0 - 2 \\ y \;=\; 7 & y \;=\; 2 & y \;=\; -1 & y \;=\; -2 \end{matrix} $$
$$ \begin{matrix} x \;=\; -3 & x \;=\; -2 & x \;=\; -1 \\ y \;=\; (-3)^{2-2} & y \;=\; (-2)^{2-2} & y \;=\; (-1)^{2-2} \\ y \;=\; 9-2 & y \;=\; 4 - 2 & y \;=\; 1 - 2 \\ y \;=\; 7 & y \;=\; 2 & y \;=\; -1 \end{matrix} $$
The coordinates of the points to plot are (-3, 7), (-2, 2), (-1, -1), (0, -2), (1, -1)
Now use these coordinates points to plot a graph.
PASTE THE GRAPH HERE!
What is the difference between grid and surface coordinates?
The grid coordinates and surface coordinates are both related in coordinate representation but in different contexts and scales in coordinate geometry. Their differences are
Grid Coordinates
Grid coordinates are the points that are located on a cartesian coordinate system in a two-dimensional plane. The two-dimensional system consists of a horizontal x-axis and a vertical y-axis that intersect at the origin (0, 0) on a graph.
It is used to plot points, lines, and curves in a 2-D plane because it is used in various applications such as plotting locations on maps, navigation systems, and computer graphics.
Surface Coordinates
Surface coordinates are used to describe points on a three-dimensional surface. They can refer to spherical or cylindrical coordinates to various coordinate systems that are present in three-dimensional Cartesian coordinates (x, y, z) space.
In Spherical Coordinates, its coordinates are (ρ, θ, φ) instead of (x,y,z), where ρ is the radius, θ is the angle, and φ is the polar angle. In Cylindrical Coordinates its coordinates are (r, θ, z), where r is the radial distance, θ is the angular coordinate, and z is the height.
How to convert grid coordinates to longitude and latitude?
For the conversion of grid coordinates to geographic coordinates (longitude and latitude) is a geospatial application that depends on the specific projection and coordinate system used in the grid coordinates. Here are some steps to describe on how to perform this conversion:
- Identify the Grid Coordinate System that includes the Universal Transverse Mercator (UTM), State Plane Coordinate System (SPCS), or other local systems.
- Determine the projection of the curved surface (that curved form after finding the coordinates points on a graph) of Earth into a flat plane.
- Then use the Geographic Information System (GIS) software and it provides the corresponding longitude and latitude.
How to do rotations on a coordinate grid?
For the rotation of a point or a shape on a coordinate grid, first find the changing position based on a given angle on a specific point at the origin (0, 0). Lets us see how to perform rotations on a coordinate grid:
When you rotate a point (x,y) around at the origin by an angle θ, the new coordinates (x′,y′) can be found using the following formulas:
- $$ x′ \;=\; xcos(θ) − ysin(θ) $$
- $$ y′ \;=\; xsin(θ) + ycos(θ) $$
Steps for Rotation:
- Identify the Rotating points as P(x,y).
- Find the Angle of Rotation θ(in degrees or radians) by which you want to rotate that point.
- If your angle θ is in degrees, then convert it to radians using the formula θ radians = θ degrees × 180π.
- Then use the rotation formulas to calculate the new coordinates (x′, y′).
When a rectangle is graphed on a coordinate grid which transformation occurs?
When a rectangle is graphed on a coordinate grid, various transformations can be applied to it, which are the rotations, reflections, and dilations. This transformation affects the position, orientation, or size of the rectangle in a specific way.
- Translation:
When the rectangle translates without changing its shape, size, or orientation, each vertex (x, y) of the rectangle is moved with the same distance in one direction then after translation(a, b) new vertices are (x + a, y + b).
- Rotation:
When you rotate the rectangle around at the origin, for a certain angle the orientation of the rectangle changes, but its shape and size remain the same.
If a point (x, y) is rotated around the origin by an angle θ, the new coordinates (x′, y′) are x′ = x cos(θ) − y sin(θ).
- Reflection:
When you flip the rectangle over a specified axis (x-axis, y-axis, or another line), the orientation of the rectangle changes to its mirror image. Reflection over the x-axis (x, y) becomes (x, −y).Reflection over the y-axis (x, y)becomes (−x, y) and over the line y=x,(x,y) becomes (y, x).
- Dilation:
When you resizing the rectangle by expanding or contracting it at the origin point, usually the shape of the rectangle remains the same, but its size changes.
If the rectangle is dilated by a scale factor k, the new coordinates (x′,y′) are x′ = kx, y′ = ky. However, each transformation changes the position, orientation, or size of the rectangle on the coordinate grid. By applying these transformations, you can manipulate the rectangle for different mathematical analyses.
