Return to more free geometry help or visit t he Grade A homepage. Return to the top of basic transformation geometry. This is typically known as skewing or distorting the image. In a non-rigid transformation, the shape and size of the image are altered. You just learned about three rigid transformations: This type of transformation is often called coordinate geometry because of its connection back to the coordinate plane. Rotation 180° around the origin: T( x, y) = (- x, - y) In the example above, for a 180° rotation, the formula is: Some geometry lessons will connect back to algebra by describing the formula causing the translation. That's what makes the rotation a rotation of 90°. Also all the colored lines form 90° angles. Notice that all of the colored lines are the same distance from the center or rotation than than are from the point. The figure shown at the right is a rotation of 90° rotated around the center of rotation. Also, rotations are done counterclockwise! You can also use this page to find sample questions, videos. You can rotate your object at any degree measure, but 90° and 180° are two of the most common. Install and practice the educational apps related to Reflection, Rotation and Translation. Reflection over line y = x: T( x, y) = ( y, x)Ī rotation is a transformation that is performed by "spinning" the object around a fixed point known as the center of rotation. Reflection over y-axis: T(x, y) = (- x, y) Reflection over x-axis: T( x, y) = ( x, - y) In other words, the line of reflection is directly in the middle of both points.Įxamples of transformation geometry in the coordinate plane. The line of reflection is equidistant from both red points, blue points, and green points. Notice the colored vertices for each of the triangles. Let's look at two very common reflections: a horizontal reflection and a vertical reflection. The transformation for this example would be T( x, y) = ( x+5, y+3).Ī reflection is a "flip" of an object over a line. More advanced transformation geometry is done on the coordinate plane. In this case, the rule is "5 to the right and 3 up." You can also translate a pre-image to the left, down, or any combination of two of the four directions. The formal definition of a translation is "every point of the pre-image is moved the same distance in the same direction to form the image." Take a look at the picture below for some clarification.Įach translation follows a rule. The most basic transformation is the translation. Translations - Each Point is Moved the Same Way Enlarge the triangle by a scale factor of 2.The original figure is called the pre-image the new (copied) picture is called the image of the transformation.Ī rigid transformation is one in which the pre-image and the image both have the exact same size and shape. If the scale factor is 1/2, draw lines which are 1/2 as long, etc. If the scale factor is 3, draw lines which are three times as long. Measure the lengths of each of these lines.Ģ) If the scale factor is 2, draw a line from the centre of enlargement, through each vertex, which is twice as long as the length you measured. The resultant position of the shape on the tracing paper is where the shape is rotated to.Įnlargements have a centre of enlargement and a scale factor.ġ) Draw a line from the centre of enlargement to each vertex ('corner') of the shape you wish to enlarge. Push the end of your pencil down onto the tracing paper, where the centre of rotation is and turn the tracing paper through the appropriate angle (if you are not told whether the angle of rotation is clockwise or anticlockwise, it would usually be anticlockwise). If you wish to use tracing paper to help with rotations: draw the shape you wish to rotate onto the tracing paper and put this over shape. When describing a rotation, the centre and angle of rotation are given. The distance of each point of a shape from the line of reflection will be the same as the distance of the reflected point from the line.įor example, below is a triangle that has been reflected in the line y = x (the length of the pink lines should be the same on each side of the line y=x): When describing a reflection, you need to state the line which the shape has been reflected in. A reflection is like placing a mirror on the page.
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