This lesson will teach you how to test for symmetry. You can test the graph of a relation for symmetry with respect to the x-axis, y-axis, and the origin. In this lesson, we will confirm symmetry algebraically.

Test for symmetry with respect to the x-axis.

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Wine for mac os high sierra. The graph of a relation is symmetric with respect to the x-axis if for every point (x,y) on the graph, the point (x, -y) is also on the graph. To check for symmetry with respect to the x-axis, just replace y with -y and see if you still get the same equation. If you do get the same equation, then the graph is symmetric with respect to the x-axis.

Example #1:
is x = 3y⁴ - 2 symmetric with respect to the x-axis?
Replace y with -y in the equation.
X = 3(-y)⁴ - 2
X = 3y⁴ - 2

Since replacing y with -y gives the same equation, the equation x = 3y⁴ - 2 is symmetric with respect to the x-axis.

1. To enter the serial number: 1 Open an existing Photoshop file or create a new file. 2 If the color mode of the document is not RGB Color or CMYK Color, choose either one of these modes in the Image Mode menu. 3 Launch SymmetryShop by choosing File Automate Artlandia SymmetryShop. 4 Click the Register button. 5 Fill in the serial number.
2. Download Artlandia SymmetryShop The free demo (tryout) version and the full version of Artlandia SymmetryShop are one and the same. The plug-in works in the trial mode until you unlock the full version by entering a serial number.

Test for symmetry with respect to the y-axis.

The graph of a relation is symmetric with respect to the y-axis if for every point (x,y) on the graph, the point (-x, y) is also on the graph.
To check for symmetry with respect to the y-axis, just replace x with -x and see if you still get the same equation. If you do get the same equation, then the graph is symmetric with respect to the y-axis.

Symmetryshop Serial Number

Example #2:
is y = 5x² + 4 symmetric with respect to the x-axis?
Replace x with -x in the equation.
Y = 5(-x)² + 4
Y = 5x² + 4

Since replacing x with -x gives the same equation, the equation y = 5x² + 4 is symmetric with respect to the y-axis.

Test for symmetry with respect to the origin.

The graph of a relation is symmetric with respect to the origin if for every point (x,y) on the graph, the point (-x, -y) is also on the graph.
To check for symmetry with respect to the origin, just replace x with -x and y
with -y and see if you still get the same equation. If you do get the same equation, then the graph is symmetric with respect to the origin.

Example #3:
is 2xy = 12 symmetric with respect to the origin?
Replace x with -x and y with -y in the equation.
2(-x × -y) = 12
2xy = 12
Since replacing x with -x and y with -y gives the same equation, the equation
2xy = 12 is symmetric with respect to the origin.

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Introduction

Creating patterns in Adobe Photoshop is not as inspiring a task as I would have liked it to be --you need to use the Edit | Define Pattern option and that merely gives you a copy of the definedarea. Photoshop by itself has few options to create repeating symmetrical patterns -- and thoseoptions can be time-consuming as well. Artlandia SymmetryShop aims to fulfill that void -- and onceyou understand how it works, it's everything you could have wanted in an automatic pattern creator.

About Symmetry Shop

SymmetryShop is a Adobe Photoshop plug-in from Artlandia that works from within Photoshop'sAutomate submenu. Artlandia, an Illinois, USA based company creates graphic design software to createpatterns -- they also sell patterns.

Other than SymmetryShop, Artlandia also creates SymmetryWorks, a similar add-in that works fromwithin Adobe Illustrator. You can learn more about Artlandiaat their site.

Download and Installation

You can download the plug-in file for SymmetryShop from the Artlandia website. It's actually a zipfile that you need to unarchive and place in Photoshop's plug-in folder -- make sure that you quitPhotoshop before copying the plug-in -- the plug-in will be available inside Photoshop's File |Automate submenu the next time you run Photoshop.

The steps detailed work identically for both the Windows or Mac versions of SymmetryShop -- forthis tutorial, we are using the Windows version.
By default, the plug-in runs in a demo mode that limits which configuration options you can change andapply -- the full, registered version has no such limitations. Registration provides you with anArtlandia online account and an unlock key -- the unlock key is tied to your Photoshop serial numberso if you upgrade or change your version of Photoshop, you'll have to get in touch with Artlandia'ssupport department.

How To Use

Here's how you can create symmetrical patterns using this Photoshop plug-in.

1. Open a new document in Photoshop and create a shape on it -- apply a solid color or gradient,for this tutorial we are using a gradient overlay as you can see in Figure 1.Alternatively, just open any image -- the SymmetryShop plug-in folder also includes some sampleimages.
   Figure 1: A sample image to start with
   
2. Now, choose File | Automate | Artlandia SymmetryShop as shown in Figure 2.
   Figure 2: The Artlandia SymmetryShop menu option
   SymmetryShop works only with raster images -- since a vector shape have been created in the layer,SymmetryShop shows a warning message that asks you to rasterize the shape layer -- accept this optionby clicking the OK button.
   
   Note: Patterns in SymmetryShop are created on the basis of a found selection orworkpath. If SymmetryShop is not able to find selection or the workpath it will select it on its ownand proceed to create a pattern out of it.
   
   
3. You will now see the SymmetryShop interface as shown in Figure 3.
   Figure 3: The SymmetryShop interface
   The interface is divided in six parts -- these are quite easy to use, as explained below:
   
   1. Symmetry Control has all the different default pattern algorithms -- forexample mirror, kaleidoscope, etc., which can be applied by choosing any of them.
      
   2. Layouts are presets that let you create some of the most commonly used types ofpatterns with a single click -- examples include brick, diamond, gradation, etc.
      
   3. Clip at Control Path allows you to change the required gap parameter betweenthe repeating patterns by using the Overlap slider, and can make softer edges by using the Featherslider.
      
   4. Tiling: Use this option to create number of repetition on the X and Y axes --this is only really useful if you are applying the pattern to the existing image -- for all practicalreasons, it's so much more easier to create a reusable pattern in Photoshop. Show isfor previewing the path or the selection found to create pattern.
      
   5. Preferences opens a new dialog box that you can see in Figure 4and Undo is to revert to the previous state.
      Figure 4: Preferences
      
   6. Control Path allows you to choose an area of the image from where the the pathor the selection for the pattern is procured -- I feel this is not as intuitive as it should have been-- entering pixel coordinates can be a process of trial and error and there should have been arrowkeys that allowed you to nudge the selection. SymmetryShop also allows to scale, skew, and rotate theselection.
      
   Note: Let the Preview check box be activated to see the changes being applied to theshape and ensuing pattern.
   
   
4. After making the changes click OK to apply the pattern to active Photoshopdocument or choose Export to add the created pattern into your current Photoshoppatterns, so that it can be used in the future as well.
   

Figure 5 below shows a shape and the sample pattern created from a shape usingSymmetryShop in Adobe Photoshop. As you can see, the possibilities are endless.
Figure 5: A shape and a pattern

SymmetryShop really shines when you select something in the artwork rather than letting the plug-into select a simple geometric region for you as we did in this review for reasons of simplicity. Then,you can create patterns like what you can see in Figure 6.

Symmetryshop Serial Search

Figure 6: A more intricate pattern

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