Tips on using Paths Option In Adobe Illustrator :

Let us view the NINE various options under Paths in Object Menu namely > 1. Join / 2. Average / 3.Outline Stroke / 4.Offset path / 5.Devide Objects Below / 6.Simplify / 7.Add Anchor Objects / 8.Split into Grid and 9.Clean up. This is not a tutorial teaching all the topics under this option. This involves only certain topics under the Paths option. The purpose of this article is to provide tips for using certain sub-options of Paths option.Open a new document in Adobe Illustrator. First Draw 2 Lines using the line tool. The lines are not visible so apply stroke color. I also increased the line thickness (stroke size) so that the lines can be visible properly. Once the Two lines are drawn, Use the Direct Selection Tool and select the corner points that you want to join (not the whole parts of the lines).

• Join : Now, go to Object Menu > Paths > Join. You will have the result as seen in the image A.The two lines are Joined by another line. Refer image A

• Average > Horizontal : Again draw two lines and select the corners that have to be joined using Direct selection tool. This time use the option, Object Menu >Paths > Average and select the sub-option called > Horizontal. Please view the image B for referance on the position in which the items are placed. The result is that, both the lines are joined by another line and the straight lines become Diagonal.Refer image B.  Average > Vertical : The lines when selected using (Direct Selection tool) in the corners and using this option under Object Menu >Paths > Average > Vertical option, they tend to extend a little. But, if you rotate the lines to change the position of the lines as seen in the image C, the diagonal lines which intersect each other result in a single vertical line. Refer image C.

• Outline stroke : this is not selecting particular points of a line. You need not select multiple lines. This simply darkens the stroke of the line.

• Offset Path : This option creates another copy of the shape selected. The copy consists of change in the corners. The corners can look like curves/ Polygonal/Rounded rectangle.          ((A.)) Using Text > First to see the corner effects, we can use the text as seen in image D. First type a Text. Select the text, using ordinary Selection Tool. Go to Type Menu > select 'Create Outlines' option. This option enables us to select the Text using Direct selection tool and reshape it. Select the outlined Text using direct selection tool and  Now use, Object Menu >Paths > Offset Path. The offset distance is the distance form the actual shape. The more the offset distance, the thicker / larger the shape would become. under Joins, there are three options namely - Millter > Which gives extra thickness (according to offset size) at the same style as that of the text for the corners of a text, second there is - Round > which gives Rounded curvey look for the corners of the text and the third is the - Bevel > which gives a Polygonal look. I have circled the areas to show the effect under each option.The effects of these three can be seen in the image D. ((B.)) Using Shapes > Next, we shall use the same option on simple shape. Create a shape using rectangle shape tool. The effect of these can be seen in  image E. As i mentioned above, a copy would be made. I will show you what can be done with the copy. For the next one, as seen in the image F, i applied Bevel offset path option so that the shape has polygonal corners. The resulted shape is bigger than the original shape (as the offset distance given is greater than Zero. If Zero is given, you will have same size as that of the original shape.). Select the original shape which is present behind and hidden by the resulted shape by clicking in the center. Once the original shape is selected, use Object Menu >Paths > Divide Objects below ( I have explained about it below). Now use the selection tool and move the original, the resulted shape is cut by the original shape.This can be decorated and used as a frame for an image. View image F1 and F2 for referance.

• Divide Objects Below : From above you might have understood about this option. Under this, one shape is used as a Knife to cut another shape.The positions in which the objects are placed can result in various types of intersections.((A.)) Position at Corners > Position 1 > Draw two shapes, one rectangle of color red and square of color green, and place the green shape on top of the red shape.Select the Green shape using selection tool and use, Object Menu >Paths > Divide Objects below option. you will notice that the green shape has dissappeared and there is an intersection mark on the red shape.Using selection tool, you can move the entire red shape, BUT use the Direct Selection tool to move and you can see that the two parts are seperated. In this example, the green shape acts as a knife. Refer image G. The result shown is in the order of the steps written. ((B.)) Position at Corners > Position 2 > Draw two shapes, one rectangle of color red and square of color green, and place the green shape on top of the red shape. This time, Select the Red shape using selection tool and use, Object Menu >Paths > Divide Objects below option. you will notice that the Red  shape has totally dissappeared and there is an intersection mark on the rgreen shape.Similarly as above, use the Direct Selection tool to move and you can see that the two parts are seperated. In this example, the Red shape acts as a knife. Refer image H. The result shown is in the order of the steps written.((C.)) Position at Centre > Position 1 > Now we shall draw another set of rectangle shapes as seen in the image I. One is Purple and the other one is Blue.Place the Blue shape over the purple shape. Select the Blue shape and use the ' Divide Objects Below'' option. The blue shape acts as a knife and dissappears.When moved using Direct selection tool, you can see a hole on the Purple shape. Similarly, you can reverse the process by selecting the Purple object and using the ' Divide Objects Below'' option. Refer image I.((D.)) Position at Centre > Position 2 > Use the same setting as above but create another copy of the Blue shape by using, ALT + click the shape and drag. Now position them as seen in the image. Select the purple shape and used the ' Divide Objects Below'' option. The puple shape acts as a knife and both the blue shapes are cut and can be moved using Direct selection tool. Refer image J. Similarly, you can reverse the procedure. To select multiple shapes, use, SHIFT + select the required shapes.

• Simplify : This is not suited for lines. Can be used for shapes or Outlined Text.This option can be used to change the shape's curves a little different in referance to the actual shape size. the difference between using this option and the Direct selection tool or Convert point tool (which is also used to reshape objects) is that in direct selection tool, you randomly reshape, but here you can use the original shape as referance and reshape accordingly.
• Add anchor points : using this option, you can add anchor points to lines / shapes, which by using the Direct selection tool can alter their shapes. First select the anchor points using direct selection tool and using the same tool, click and drag in different directions, to reshape.

• Split into Grid : A particular shape within the size of the shape, can be split, any number of times. To enter correct values for the splitting purpose, you have to know what the values stand for. Refer the following image to understand the different terms such as, Row width / Row Height / column width / column height / gutter etc. stand for.

• Clean up : Clean up can be used for stray points, Unpainted objects, Empty text paths. (a.) Stray points > when you draw a line using a line tool and you delete the line, but some anchor points of the line may not be removed. It is difficult to search for them. You can use the clean up > stray points to remove them in the document. you may not see the effect of removal but, suppose you select one stray point and use this option, you can see the stray point removal. (b.) Unpainted Objects  > Suppose you draw a shape without fill or stroke, they are present in the page but are not visible. those shapes are of no use so they can be removed. Again, to see the removal effect with your own eyes, you might have to select one shape without fill and use this option, you can see the shape removal. (c.) Empty Text paths > You might select the text tool and directly draw a shape / path to type the text in, but you do not type anything. Such shape created for typing text but has no text is of no use and can be removed. Select any text paths and use cleanup to see the removal effect to understand better.

These are all the NINE various options under Object Menu > Paths.