Enlargement G12F
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The document discusses enlargements of shapes using scale factors and centers of enlargement. It provides examples of enlarging triangles with different scale factors (both positive and negative) and centers of enlargement both inside and outside the original shape. It also discusses how to find the center of enlargement given a original and enlarged shape. The key steps in enlargement are drawing lines from the center of enlargement to each vertex, calculating new positions by multiplying distances from the center by the scale factor, and joining the new points.
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The document discusses enlargements in transformation geometry. It defines an enlargement as a transformation that changes the size and position of a shape. For an enlargement, all lengths are multiplied by a scale factor while all angles remain unchanged. The scale factor k denotes the number by which an object is enlarged. To perform an enlargement, you need a center of enlargement and the scale factor. The document provides examples and step-by-step instructions for performing enlargements using the ray method. It also discusses properties of enlargements and how to find the center of enlargement given an enlarged shape.
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Introduction to objective, scope and outcome the subject
Chapter 2
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Chapter 3
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Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
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Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
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2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
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Enlargement G12F
- 1. Enlargements Objectives To be able to: Enlarge shapes given a scale factor and centre of enlargement. Find centres of enlargement
- 2. Scale factors and centres of enlargement The size of an enlargement is described by its scale factor. For example, a scale factor of 2 means that the new shape is twice the size of the original , a scale factor of (-2) means that the new shape is reflect twice the size of the original. The position of the enlarged shape depends on the centre of enlargement.
- 3. How do I enlarge a shape? Enlarge triangle A with a scale factor of 3 and centre of enlargement c(2,1) Draw lines from the centre of enlargement to each vertex of your shape Calculate the distance from the C to a vertex and multiply it by the scale factor to find its new position Repeat for all the other vertices Join up your new points to create your enlarged shape 0 1 2 3 4 5 6 7 8 9 10 x 1 9 8 7 6 5 4 3 2 y 10 A A’
- 4. How do I enlarge a shape? Enlarge triangle A with a scale factor of -2 and centre of enlargement c(8,6) Draw lines from the centre of enlargement to each vertex of your shape Calculate the distance from the C to a vertex and multiply it by the scale factor to find its new position Repeat for all the other vertices Join up your new points to create your enlarged shape 0 1 2 3 4 5 6 7 8 9 10 x 1 9 8 7 6 5 4 3 2 y 10 A A’
- 5. What if the centre of enlargement is inside the shape? Enlarge shape B with scale factor 2 and centre of enlargement (6,6) B B’ 0 1 2 3 4 5 6 7 8 9 10 x 1 9 8 7 6 5 4 3 2 y
- 6. What about fractional scale factors? D Enlarge shape D by scale factor ½ and centre of enlargement (10,1) Even though the shape gets smaller, it’s still called an enlargement. Each vertex on the enlarged shape is half the distance from the C than its corresponding vertex on the original shape. 0 1 2 3 4 5 6 7 8 9 10 x 1 9 8 7 6 5 4 3 2 y
- 7. How do I find the centre of enlargement? Join up the corresponding vertices and extend the lines The point where they all intersect is your centre of enlargement C C (2,9) What was the scale factor of enlargement? 0 1 2 3 4 5 6 7 8 9 10 x 1 9 8 7 6 5 4 3 2 y 10 E