![]() ![]() ![]() Reflection and glide reflection are opposite isometry. From the four types of transformations translation, reflection, glide reflection, and rotation. Distance remains preserved but orientation (or order) changes in a glide reflection. Reflection transformation is an opposite isometry, and therefore every glide reflection is also an opposite isometry. Look at our example of this concept below.Īn opposite isometry preserves the distance but orientation changes, from clockwise to anti-clockwise (counter clockwise) or from anti-clockwise(counter clockwise) to clockwise. Whether you perform translation first and followed by reflection or you perform reflection first and followed by translation, outcome remains same.įor example, foot prints. Outcome will not affect if you reverse the composition of transformation performed on the figure. Commutative properties:Ī glide refection is commutative. Glide reflection occurs when you perform translation (glide) on a figure and followed by a reflection across a line parallel to the direction of translation. Glide reflections are essential to an analysis of symmetries. A glide reflection is – commutative and have opposite isometry. Glide reflection is the composition of translation and a reflection, where the translation is parallel to the line of reflection or reflection in line parallel to the direction of translation. Every point is the same distance from the central line after performing reflection on an object. Reflection means reflecting an image over a mirror line. Translation simply means moving, every point of the shape must move the same distance, and in the same direction. Therefore, Glide reflection is also known as trans-flection. First, a translation is performed on the figure, and then it is reflected over a line. 360° rotation: x and y-values remain the same.Definition: A glide reflection in math is a combination of transformations in 2-dimensional geometry.180° rotation: x and y-values remain the same but have opposite signs.90° rotation: x and y-values interchange.If you are using a small screen, please rotate your screen to have a better view of the table below!! Processįrom the table above, we can summarise that: We will explain rotation by summarising the methods or rules in the table below: Shrinking: \(k\) is a decimal number (a fraction).What was the x-value will now become the y-value and what was the y-value will now become the x-value.ĭilation is about changing the size of the object either by enlarging or shrinking by a factor. Reflection in the line y = x, simply requires you to interchange the values. When reflecting in the y-axis, the y-values remain constant while the x-values change the sign. When reflecting in the x-axis, the x-values remain constant while the y-values change the sign.Īs we can see from this result, the new point is the opposite side of the y-axis. In reflection transformations, each point in an object appears at an equal distance on the opposite side of the line of reflection. In this transformation, an object will be reflected across a line, creating an image. ![]() Where \(b\) is positive when an object is moved up and negative when moved down. Vertical translationįor the vertical translation, the function will either move up or down. For example, a shift of 6 units to the left means that you should count six numbers to the left of your point. In a graph, the results can be obtained simply by moving according to number stated for the translaton. The sketch below shows the results of the above example. Where \(a\) is positive when an object is moved to the right and negative when moved to te right. Horizontal translation moves objects leftwards or rightwards. Where \(a\) and \(b\) are parameters that for horizontal and vertical shifting, respectively. Translations move objects either horizontally of vertically. When you translate objects/functions, you are moving them to a new point. The general rule or notation for transformation geometry is that a new point is called an image, symbolised with an apostrophe (') next to the name of a point, i.e,: As you get to higher grades, you will apply these processes to functions/graphs. ![]() Now that you are in grade 9, transformation geometry will be about creating an image of a shape by performing the above procesess. At that time, you will only be asked about these processes in the exams and they will never be covered again in class. These notes or concept, you will use until grade 12. Grade 9 syllabus introduces you to transformation geometry which involves translation, reflection, dilation and rotation. Transformation geometry involves making images or copies of an object. ![]()
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