![]() ![]() Enlarge the triangle by a scale factor of 2. ![]() 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 shape or line in question is usually graphed on a coordinate plane. Basically, when we have a shape or line and we mess around with it a bit, it is a transformation. 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): Transformations: When we take a shape or line and we flip it, rotate it, slide it, or make it bigger or smaller. When describing a reflection, you need to state the line which the shape has been reflected in. To form DEF from ABC, the scale factor would be 2.A reflection is like placing a mirror on the page. Assuming that ABC is twice the size of DEF, the scale factor to form ABC from DEF would be 0.5. There are several types of transformations that can be applied to a. The scale factor that would be used to form DEF from ABC is the reciprocal of the scale factor that would be used to form ABC from DEF. CREDITSAnimation & Design: Waldi ApollisNarration: Dale BennettScript: Phoebe Barker, Matilda Denbow, Lexie HoyerWhich is actually pretty much what it also m. In geometry, transformations are changes that are made to a geometric shape or figure. Each of the corresponding sides is proportional, so either triangle can be used to form the other by multiplying them by an appropriate scale factor. The triangles are not congruent, but are similar. Transformations are a process by which a shape is moved in some way, whilst retaining its identity. In the above figure, triangle ABC or DEF can be dilated to form the other triangle. DilationĪ dilation increases or decreases the size of a geometric figure while keeping the relative proportions of the figure the same. A rotates to D, B rotates to E, and C rotates to F. RotationĪ rotation turns each point on the preimage a given angle measure around a fixed point or axis.Įach point on triangle ABC is rotated 45° counterclockwise around point R, the center of rotation, to form triangle DEF. Starting from the concept of the circle, I show that a large variety of shapes can be described by a single and simple geometrical equation, the Superformula. ReflectionĪ reflection produces a mirror image of a geometric figure. TranslationĪ translation moves every point on the preimage the same distance in a given direction. In non-rigid transformations, the preimage and image are not congruent. ![]() The following diagram shows the shape A which is translated to give the shapes B, C. Only position or orientation may change, so the preimage and image are congruent. (c) Write down the coordinates of the corners of the translated triangle. Rigid transformations are transformations that preserve the shape and size of the geometric figure. Translation, reflection, and rotation are all rigid transformations, while dilation is a non-rigid transformation. Types of transformationsīelow are four common transformations. In a transformation, the original figure is called the preimage and the figure that is produced by the transformation is called the image. In geometry, a transformation moves or alters a geometric figure in some way (size, position, etc.). Home / geometry / transformation Transformation ![]()
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