Textlab 1 0 7 – A Text Transformation Tool

The TextLab is a text transformation tool, which is suggesting what operations can be performed based on your input. For example, if you copy and paste JSON into the application, it suggests to validate and format that JSON. This XSL Transformer (XSLT) let's you transform an XML file using an XSL (EXtensible Stylesheet Language) file. You can also chose your indentation level if the result is an XML file. Thanks a million to Bram Ruttens aka 'skeltavik' for identifying security issues in this tool.

Rectangular Coordinate System

The rectangular coordinate systemA system with two number lines at right angles uniquely specifying points in a plane using ordered pairs (x, y). consists of two real number lines that intersect at a right angle. The horizontal number line is called the x-axisThe horizontal number line used as reference in the rectangular coordinate system., and the vertical number line is called the y-axisThe vertical number line used as reference in the rectangular coordinate system.. These two number lines define a flat surface called a planeThe flat surface defined by the x- and y-axes., and each point on this plane is associated with an ordered pairA pair (x, y) that identifies position relative to the origin on a rectangular coordinate plane. of real numbers (x, y). The first number is called the x-coordinate, and the second number is called the y-coordinate. The intersection of the two axes is known as the originThe point where the x- and y-axes cross, denoted by (0, 0)., which corresponds to the point (0, 0).

An ordered pair (x, y) represents the position of a point relative to the origin. The x-coordinate represents a position to the right of the origin if it is positive and to the left of the origin if it is negative. The y-coordinate represents a position above the origin if it is positive and below the origin if it is negative. Using this system, every position (point) in the plane is uniquely identified. For example, the pair (2, 3) denotes the position relative to the origin as shown:

Portrait of René Descartes (1596–1650) after Frans Hals, from http://commons.wikimedia.org/wiki/File:Frans_Hals_-_Portret_van_Ren%C3%A9_Descartes.jpg.

This system is often called the Cartesian coordinate systemUsed in honor of René Descartes when referring to the rectangular coordinate system., named after the French mathematician René Descartes (1596–1650).

The x- and y-axes break the plane into four regions called quadrantsThe four regions of a rectangular coordinate plane partly bounded by the x- and y-axes and numbered using the roman numerals I, II, III, and IV., named using roman numerals I, II, III, and IV, as pictured. In quadrant I, both coordinates are positive. In quadrant II, the x-coordinate is negative and the y-coordinate is positive. In quadrant III, both coordinates are negative. In quadrant IV, the x-coordinate is positive and the y-coordinate is negative.

Example 1: Plot the ordered pair (−3, 5) and determine the quadrant in which it lies.

Textlab 1 0 7 – A Text Transformation Tool Tutorial

Solution: The coordinates x=−3 and y=5 indicate a point 3 units to the left of and 5 units above the origin.

Answer: The point is plotted in quadrant II (QII) because the x-coordinate is negative and the y-coordinate is positive.

Ordered pairs with 0 as one of the coordinates do not lie in a quadrant; these points are on one axis or the other (or the point is the origin if both coordinates are 0). Also, the scale indicated on the x-axis may be different from the scale indicated on the y-axis. Choose a scale that is convenient for the given situation.

Example 2: Plot this set of ordered pairs: {(4, 0), (−6, 0), (0, 3), (−2, 6), (−4, −6)}.

Solution: Each tick mark on the x-axis represents 2 units and each tick mark on the y-axis represents 3 units.

Example 3: Plot this set of ordered pairs: {(−6, −5), (−3, −3), (0, −1), (3, 1), (6, 3)}.

Solution:

In this example, the points appear to be collinearDescribes points that lie on the same line., or to lie on the same line. The entire chapter focuses on finding and expressing points with this property.

Try this! Plot the set of points {(5, 3), (−3, 2), (−2, −4), (4, −3)} and indicate in which quadrant they lie. ([Link: Click here for printable graph paper in PDF.])

Answer:

Graphs are used in everyday life to display data visually. A line graphA set of related data values graphed on a coordinate plane and connected by line segments. consists of a set of related data values graphed on a coordinate plane and connected by line segments. Typically, the independent quantity, such as time, is displayed on the x-axis and the dependent quantity, such as distance traveled, on the y-axis.

Example 4: The following line graph shows the number of mathematics and statistics bachelor's degrees awarded in the United States each year since 1970.

a. How many mathematics and statistics bachelor's degrees were awarded in 1975?

Ordered pairs with 0 as one of the coordinates do not lie in a quadrant; these points are on one axis or the other (or the point is the origin if both coordinates are 0). Also, the scale indicated on the x-axis may be different from the scale indicated on the y-axis. Choose a scale that is convenient for the given situation.

Example 2: Plot this set of ordered pairs: {(4, 0), (−6, 0), (0, 3), (−2, 6), (−4, −6)}.

Solution: Each tick mark on the x-axis represents 2 units and each tick mark on the y-axis represents 3 units.

Example 3: Plot this set of ordered pairs: {(−6, −5), (−3, −3), (0, −1), (3, 1), (6, 3)}.

Solution:

In this example, the points appear to be collinearDescribes points that lie on the same line., or to lie on the same line. The entire chapter focuses on finding and expressing points with this property.

Try this! Plot the set of points {(5, 3), (−3, 2), (−2, −4), (4, −3)} and indicate in which quadrant they lie. ([Link: Click here for printable graph paper in PDF.])

Answer:

Graphs are used in everyday life to display data visually. A line graphA set of related data values graphed on a coordinate plane and connected by line segments. consists of a set of related data values graphed on a coordinate plane and connected by line segments. Typically, the independent quantity, such as time, is displayed on the x-axis and the dependent quantity, such as distance traveled, on the y-axis.

Example 4: The following line graph shows the number of mathematics and statistics bachelor's degrees awarded in the United States each year since 1970.

a. How many mathematics and statistics bachelor's degrees were awarded in 1975?

b. In which years were the number of mathematics and statistics degrees awarded at the low of 11,000?

Solution:

a. The scale on the x-axis represents time since 1970, so to determine the number of degrees awarded in 1975, read the y-value of the graph at x = 5.

The y-value corresponding to x = 5 is 18. The graph indicates that this is in thousands; there were 18,000 mathematics and statistics degrees awarded in 1975.

b. To find the year a particular number of degrees was awarded, first look at the y-axis. In this case, 11,000 degrees is represented by 11 on the y-axis; look to the right to see in which years this occurred.

The y-value of 11 occurs at two data points, one where x = 10 and the other where x = 30. These values correspond to the years 1980 and 2000, respectively.

Answers:

a. In the year 1975, 18,000 mathematics and statistics degrees were awarded.

b. In the years 1980 and 2000, the lows of 11,000 mathematics and statistics degrees were awarded.

Scale layers proportionally

Updated in Photoshop 21.0 (November 2019 release)

When transforming any layer type, dragging a corner handle now scales the layer proportionally by default, indicated by the Maintain Aspect Ratio button (Link icon) in the ON state in the Options bar. To change the default transform behavior to non-proportional scaling, simply turn OFF the Maintain Aspect Ratio (Link icon) button. The Shift key, while pressed, now acts as a toggle for the Maintain Aspect Ratio button. If the Maintain Aspect Ratio button is ON, the Shift key toggles it OFF while pressed and vice versa. Photoshop remembers your last transform behavior setting—proportional or non-proportional scaling—it will be your default transform behavior when you start Photoshop the next time.

From the menu bar, choose Edit (Win)/Photoshop (Mac) > Preferences > General, then select Legacy Free Transform.

TheFree Transform command lets you apply transformations (rotate, scale,skew, distort, and perspective) in one continuous operation. Youcan also apply a warp transformation. Instead of choosing differentcommands, you simply hold down a key on your keyboard to switchbetween transformation types.

Note:

If you are transforminga shape or entire path, the Transform command becomes the TransformPath command. If you are transforming multiple path segments (butnot the entire path), the Transform command becomes theTransform Points command.

Textlab 1 0 7 – A Text Transformation Tools

• Choose Edit > Free Transform.

• If you are transforming a selection, pixel-basedlayer, or selection border, choose the Move tool . Thenselect Show Transform Controls in the options bar.

• If you are transforming a vector shape or path,select the Path Selection tool . Thenselect Show Transform Controls in the options bar.

• To scale by dragging, do one of the following:
  • If the Maintain Aspect Ratio button (Link icon) is ON in the Options bar, drag a corner handle to scale the layer proportionally.
  • If the Maintain Aspect Ratio button (Link icon) is OFF in the Options bar, drag a corner handle to scale the layer non-proportionally.
  • Hold down the Shift key while transforming to toggle between proportional and non-proportional scaling behavior.

• To scale numerically, enter percentages in the Width and Height text boxes in the options bar. Click the Link icon to maintain the aspect ratio.

• To rotate by dragging, move the pointer outside the bounding border (it becomes a curved, two‑sided arrow), and then drag. Press Shift to constrain the rotation to 15° increments.

• To rotate numerically, enter degrees in the rotation text box in the options bar.

• To distort relative to the center point of the bounding border, press Alt (Windows) or Option (Mac OS), and drag a handle.

• To distort freely, press Ctrl (Windows) or Command (Mac OS), and drag a handle.

• To skew, press Ctrl+Shift (Windows) or Command+Shift (Mac OS), and drag a side handle. When positioned over a side handle, the pointer becomes a white arrowhead with a small double arrow.

• To skew numerically, enter degrees in the H (horizontal skew) and V (vertical skew) text boxes in the options bar.

• To apply perspective, press Ctrl+Alt+Shift (Windows) or Command+Option+Shift (Mac OS), and drag a corner handle. When positioned over a corner handle, the pointer becomes a gray arrowhead.

• To warp, click the Switch Between Free Transform And Warp Modes button in the options bar. Drag control points to manipulate the shape of the item or choose a warp style from the Warp pop‑up menu in the options bar. After choosing from the Warp pop‑up menu, a square handle is available for adjusting the shape of the warp.

• To change the reference point, click a square on the reference point locator in the options bar.

• To move an item, enter values for the new location of the reference in the X (horizontal position) and Y (vertical position) text boxes in the options bar. Click the Relative Positioning button to specify the new position in relation to the current position.

Note:

To undo the last handle adjustment, choose Edit > Undo.

Do one of the following to commit the transformation:

• Select a new tool.
• Click a layer in the Layers panel. (This action auto-commits changes and also selects the layer.)
• Click outside the canvas area in the document window.
• Click outside the bounding box in the canvas area.
• Press Enter (Windows) or Return (Mac OS), click the Commit button in the options bar, or double-click inside the transformation marquee.

To cancel the transformation, press Esc or click the Cancel button in the options bar.

Note:

When you transform a bitmap image(versus a shape or path), the image becomes slightly less sharpeach time you commit a transformation; therefore, performing multiplecommands before applying the cumulative transformation is preferableto applying each transformation separately.

Textlab 1 0 7 – A Text Transformation Tool Template