enlargement
Enlargement is a transformation in geometry where the size of a figure or shape is increased or decreased while maintaining its shape
Enlargement is a transformation in geometry where the size of a figure or shape is increased or decreased while maintaining its shape. It involves multiplying or dividing the lengths and measurements of the original figure by a scale factor. The scale factor represents the ratio of the corresponding lengths of the new shape to the original shape.
To perform an enlargement, you need two main pieces of information: the scale factor and the center of enlargement. The scale factor determines how much the figure will be enlarged or reduced, and the center of enlargement is the point about which the figure is expanded or contracted.
Here’s an example to illustrate an enlargement:
Let’s say we have a square with side length 4 units, and we want to enlarge it by a scale factor of 2 with the center of enlargement at the origin (0, 0).
1. Determine the new side length:
The new side length can be found by multiplying the original side length by the scale factor.
New side length = 4 units * 2 = 8 units
2. Determine the coordinates of the new square:
To find the corresponding coordinates of the new square, multiply each coordinate of the original square by the scale factor.
Original square: (0, 0), (4, 0), (4, 4), (0, 4)
New square: (0, 0), (8, 0), (8, 8), (0, 8)
3. Plot the original and new squares on a coordinate plane:
Original square:
(0, 0)———————————–(4, 0)
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(0, 4)———————————–(4, 4)
New square:
(0, 0)———————————–(8, 0)
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(0, 8)———————————–(8, 8)
In this example, the original square with a side length of 4 units was enlarged into a new square with a side length of 8 units, with the center of enlargement at the origin.
Enlargement is a fundamental concept in geometry and plays a significant role in various applications, such as map scaling, architectural design, and image resizing.
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