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Transformations

Introduction

There are four main types of transformations: Reflection Rotation Translation Resizing It is very important that you know how to apply these transformations and how to describe them fully and correctly.

Reflection

Describing Reflection is probably the easiest type of transformation. To describe a reflection, you only need to mention the line of reflection. This is the line which basically mirrors the shape. To find the line of reflection, simply connect the two same points of both shapes and locate the mid points. The line of reflection/symmetry is the line that passes through all these points. In the example on the left, there are two reflections: A > B : A is reflected in the line y=0 to create B A > C : A is reflected in the line y=x to create C Drawing When you sketch a reflection on a graph, it is usually sufficient to simply look at the graph and the line of reflection. If you do not feel confident enough to do so, you can simply draw a line from each of the points of the shape to the line of reflection so that this line is 90° to the line of reflection. Then extend the line by the same amount on the other line of the line of symmetry. The ends of these lines will be the points of the reflected shape. In the diagram, this has been done using the green lines.

Rotation

Describing Rotation involves turning the shape around a certain point on the graph.  To describe any rotation you need to mention the type of transformation (rotation), by how much the shape rotates (eg: 90° or 180°), in which direction (clockwise or counter clockwise) and the centre of rotation. In the example on the right, there are two rotations: A > B : 90° Clockwise Rotation around the origin (0,0) A > C: 180° Rotation around the origin (0,0) (For 180° rotations you do not need to mention the direction of rotation as it will be the same in both directions) Drawing You can again use the line method to draw rotations if you cannot sketch them by just looking at the co-ordinate grid. Simply draw a line from each point to the centre of rotation. Then draw a line that is the same length as the first line and that is at the same angel to the first line than the angle of rotation. In the example on the right, this has been done for the 90° rotation. All lines of the same colour are the same length and have a 90° angle.

Translation

Describing Translation is when we move a shape without changing its orientation or size. To describe a translated shape we use the phrase “translated by vector       “ where x is the horizontal and y the vertical movement. There are two examples on the left. A > B: Translated by Vector A > C: Translated by Vector Drawing Drawing translated shapes is very easy. You simply have to draw the shape in a different place. When ding so by looking at the vector, the top value is the horizontal movement (down if negative/up if positive) and the bottom value is the vertical movement (left if negative/right if positive). For the first example, this has been shown with arrows.

Resizing

Describing Resizing is when we resize the shape. This is usually called enlargement no matter if the shape becomes larger or smaller. To describe an enlargement, we need to know the centre of enlargement (the point from which the object is enlarged). We can find it by connecting the the same points from the original object and the enlarged object by lines. The points where these lines intersect is the centre of enlargement. We also need to know the scale factor by which the object is enlarged (how much bigger or smaller the object is). There are three examples on the right. A > B: Enlarged by scale factor 2 from the origin (0,0) A > C: Enlarged by scale factor -1 from the origin (0,0) (negative scale factors result in the object being rotated 180°) A > D: Enlarged by scale factor 1/2 from the origin (0,0) (fractional scale factors result in the object being smaller. Eg: scale factor of 1/2 results in half the size) Drawing Resizing shapes is relatively easy. Simply draw a line from the centre of enlargement to each point of the shape as has been done with the green lines in the example. Now measure the distance length of this line and multiply it by the scale factor. So if we have a scale factor of two and the point of the shape is 1 away from the centre of enlargement, the new point will be 2 away from the centre of enlargement. The same also works for fractional scale factor just that the object will become smaller. If you are pretty confident you can also just use the coordinates so that you do not have to draw lines all the time. When you have a negative scale factor just imagine it was positive and then rotate the enlarged shape by 180°.

Learn About Coordinate Geometry

Now you should master the basics of transformations. Next you should try to learn a bit about coordinate geometry to improve your knowledge and skills with coordinate planes. You can also select a completely different topic from our library. Please share this page if you like it or found it helpful!
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Chapter 32:  Learning Outcomes Students will learn how to carry out numerous transformations including reflection, resizing, rotation and translation!

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