![]() ![]() 360° rotation: x and y-values remain the same.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,: So, the rule that we have to apply here is. Solution : Step 1 : Here, the given is rotated 180 about the origin. If this figure is rotated 180 about the origin, find the vertices of the rotated figure and graph. As you get to higher grades, you will apply these processes to functions/graphs. Let P (-2, -2), Q (1, -2), R (2, -4) and S (-3, -4) be the vertices of a four sided closed figure. 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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