Enlargement scale factor 2. C is the point (5, 5).

Enlargement scale factor 2 Solution: (i) \(\frac{X’Y’}{XY}\) = k. The centre of enlargement is the point about which a shape is enlarged. They can be written as either ratios, decimals, fractions or percentages. Each side of the dark blue shape is 2 × longer than the corresponding side of the light blue shape. Its surface area is now 6 × 4cm 2 = 24cm 2 which is 4 times as large as before. The scale factor is called liner scale factor; By measurement OA=1 . 5 times longer. Find: (i) X’Y’ if XY = 4 cm, (ii) XZ if X’Z’ = 15 cm, (iii) OX’ and XX’ if OX = 3 cm. Hence OA’ / OA = OB’ / OB = OC’ / OC = 2. What are scale factors? Scale factors are applied to alter the size of the image. Consider the original triangle and the scale drawing enlargement. A Real Example of a Scale Factor A scale factor is easier to understand with an example. For example, a scale factor of \(2\) means that the new shape is twice the size of the original. Upgrade. c) Multiply these distances by your scale factor and change the directions. Title: Print Layout - Mathster Created Date: 20140105114044Z 4. All the sides double in length How does a scale factor work? When describing an enlargement you must state by how much the shape has been enlarged. For the full list of videos and more revision resources vis GCSEMathsRevision. For every enlargement, a scale factor must be specified. If the scale factor is ½ then the lengths will be halved. If the scale factor is between 0 and 1, the image is a reduction. this will remind you that the distances away from the CoE carry on in the opposite direction for a negative scale factor. GCSE transformations: enlargement by positive and negative scale factor. For example, if the distance from the centre of enlargement to one of your corners is 3 squares right and 7 squares up, and the scale factor of For example, a scale factor of 3 means you have to multiply all side lengths by 3. The picture below shows a dilation with a scale factor of 2. Option 3. Triangle ABC is the object and triangles A’ B ‘C ‘Its image under enlargement scale factor 2. Therefore, compared to the centre of enlargement, point A’ will be 2 to the right (distance x scale factor; 1 x 2) and 4 up (2 x 2). Enlarge the following shapes based on the scale factor given. enlargement s. For a shape enlarged by a scale factor of with centre of enlargement (0, I can describe an enlargement. Q5. When the scale factor, k, is less than one, the result is a reduction. Perimeter of the image = scale factor \(\times\) perimeter of the shape. A triangle XYZ has been enlarged to ∆ X’Y’Z’ about the centre of enlargement O by a scale factor 2. 5 with centre (0, 1) (Total for question = 2 marks) Q10. Share activities with pupils. A triangle is to be enlarged with scale factor 2, using the origin as the centre of enlargement. The circumstance of increase is frequently referred to as enlargement or magnification. Center of enlargement: (3, 3). Step 2: Scale factor = 3/6 (Divide each side by 6). an enlargement of scale factor . Excelling learners will be able to describe a given enlargement, Example 1 Enlarge the shape below with a scale factor of -½ with the centre of enlargement at (0, 2). The height of the vertical side on B is 6 units and on C it is 2 units. 1 Enlarge triangle T by scale factor -2 with centre of enlargement 0,0. Try placing the pin in [2] (b) On the grid, draw the image of (i) triangle A after a refl ection in the line x = –3, (ii) triangle A after a rotation about the origin through 270° anticlockwise, [2] (iii) triangle A after a translation by the vector-1-5 eo. The ratio is called scale factor of enlargement. The scale factor is commonly expressed as 1:n or 1/n, where n is the factor. The scale factor is 2. Here we call it resizing, but other people call it dilation, contraction, compression, enlargement or even expansion! Same idea, just different names. S. This means that the line will be 20 cm long after the enlargement. Finding the type of dilatation. In this case we join each point to the centre and stretch by a factor of 2. Hence, the scale factor from the larger Square to the smaller square is 1:2. The formula for the scale factor is: Scale Factor = Dimension of New Shape / Dimension of Original Shape. rotation 60° (anticlockwise) centre (0, 0). Surface Areas And Volumes Of Similar Solids Enlargements: Drag the centre of enlargement around. Scale factor 2. When asked to enlarge to a negative scale factor, students often enlarge to a positive scale factor. *Shapes are equal if their corresponding angles are equal. C is the point (5, 5). Scale Factor = Original size New size. • The center of dilation is a fixed point in the plane. Write down the scale factor for each enlargement. If the scale factor k<0, then the image will be on the opposite side of the object from the centre of enlargement. E. The full lesson and worksheet can be downloaded from https://mr-mathematics. Enlarging a 10 cm line by scale factor −2 will multiply the length by −2. e. Membership. Area of the image = (scale factor)\(^2 \times\) area of the shape; For enlargement and reduction transformations, the shape and its image Where the centre of enlargement is, and the scale factor. Negative Enlargement: A video from MathsWatch about Enlargement by a Negative Scale Factor. Plot the centre of enlargement. Below is a picture of each type of dilation (one that gets larger and one that gest smaller). In the diagram, P is the Correct answer: Example 2. Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the Enlargements: fractional scale factor (less than 1) Questions: Solutions: Enlargements: negative scale factor : Questions: Solutions: Enlargements • A description of a dilation includes the scale factor (or ratio) and the center of the dilation. A to D is scale factor 2. The answer can be checked by drawing dashed lines through pairs of corresponding State that the transformation is an enlargement. . a fraction) will make a shape smaller. 5. For example, multiplying a length by 1 ⁄ 2 will make each side half as long as it was before - which is shorter. For instance, a scale factor of -2 drawn as +2. So the two transformations are: . Example 1. 1\times2=2 . A An enlargement can be reversed by multiplying the enlarged shape by the reciprocal of the original scale factor. Share resources with colleague. When the centre of enlargement or reduction is the origin, the coordinates of the vertices of the image are scaled by the scale factor. How to Describe an Enlargement with a Negative Scale Factor Example 2 – Finding the Scale Factor The shape ABC has been enlarged to create shape A’B’C’. An image that appears upside down. An example on how to enlarge a shape by a positive and negative scale factor for GCSE revision. UNITED KINGDOM [email protected] The length of the sides of the enlarged square are So the scale factor of the enlargement must be 2. , from the centre through the object, which leads to an incorrect enlargement. • If the scale factor is Enlargement has a scale factor: The factor by which a shape is enlarged is called the scale factor. The scale factor is A to B is an enlargement scale factor 2, centre (—6, 6). To find the scale factor: Pick a side of the original shape. The centre of enlargement can be described using Cartesian coordinates. The scale factor tells us how many times larger the shape will be. Scale Factor Meaning. Give the coordinates of the centre of enlargement. Fig. You may also find problems where you are given the starting and final positions and you must For example, an enlargement of scale factor 2 has the matrix [2 0; 0 2]. Using trigonometry we find that ? = 60°. A missing length on a reduction/enlargement figure can be calculated by finding its Move the slider k so that you have an enlargement scale factor -0. Scale Factor is the ratio of dimension of size changing shape, The enlargement scale factor is a number greater than 1, indicating an increase in size or expansion of the original figure. Draw lines through the CoE and a vertex on the original object . This may be an integer or a fraction. with centre of enlargement (0, 5) Examiner Tips and Tricks. What happens when the scale factor is between 0 and 1? 3. Correct answer: Option 3. (c) From B to C The construction lines converge on (5, —1) so this is the centre of enlargement. Some enlargements produce a shape that is smaller than the original, such as an enlargement with a scale factor of ½ (where the side lengths are halved). • the sides all increase by the scale factor; • the distance of each of the vertices from the centre increases by the scale factor. Scale factors between 0 and 1 (i. Similarity criterion ABC. The scale factor is commonly denoted by r or k, which determines the amount of enlargement or reduction. 2)? 6) What scale factor maps the point E to (-4. Scale Factor = 15 inches 5 inches. To enlarge a triangle by a scale factor of -2 with the center of enlargement at (6, 7), you will go through the following steps: Identify the Vertices of the Triangle: Start with the original coordinates of the triangle's vertices. youtube. The effect of a 2 × 2 transformation matrix. 2. One vertex of the triangle is at (2, 2). centre of enlargement enlargement scale factor = 2 For every enlargement, a scale factor must be specified. Rays are often drawn in the wrong direction, i. The scale factor is found by dividing a length of a side of the enlarged How to enlarge a shape on a grid when given a scale factor. If the scale factor k=1, then the transformation is identity. 5}\times{?} = {5}\) An enlargement with a negative scale factor close scale factor The ratio of corresponding lengths in similar shapes, ie how much larger or smaller the shapes are. 5. If an enlargement has a scale factor of 2, each side of the image is 2 times larger than the sides of the object. To do this, we use a certain number to multiply the original size of the object, showing how much larger the new Enlargements: Centre of Enlargement Video 104a on www. A scale factor is the ratio between corresponding measurements of two similar 1 (Total for question 1 is 2 marks) On the grid draw an enlargement of the shaded shape with scale factor 3 2 (Total for question 2 is 2 marks) Enlargement using a negative scale factor. Label the points on the enlarged shape A’B’C’. The page concludes with practical methods for finding the scale factor by comparing corresponding sides and locating the centre of enlargement by drawing rays through corners. This means each vertex will move half the distance towards the center of enlargement. ; Its volume is now 2 3 cm 3 = 8cm 3 which is 8 times as large as before. Triangle ABC is drawn on a centimetre grid. Shape A has been enlarged by scale factor 2 to give shape B . Similar figures are identical in shape, but generally not in size. In the diagram below, shape X has been enlarged with a scale factor of 0. For example, if the scale factor is 2, the new square will be twice the size on each side. 5 centre (-2, 3). On the grid, draw an enlargement of shape A with a scale factor of 2. A Reduction Scale Factor is a number which is less than 1. The image below shows a light blue shape being enlarged to a dark blue shape. 1 Enlargement and Reduction Extra Practice 1. produces an image on the other Fill in the gap: if the scale factor of an enlargement is _____ 1, then the image is smaller than the object. For example, if you have a square with a scale factor of 2, this means that the new square will be twice the size of the original. (2) 3. The centre of enlargement is marked with a cross (x). An enlargement can be reversed by multiplying the enlarged shape by the reciprocal of the original scale factor. You can even have a scale factor of 1, which produces a shape identical to the original! Practice The figure's scale factor and type of dilatation are. Let’s choose a side that is attached to the first side. It expands. First, draw ray lines from O to each corner of the triangle. iqzkty aqesx ezfmc nje iusf bxlpdw tbded kbwau alwvycr dzavti wdmses fmvy kicjff maw ndjw