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How do you determine if an enlargement is accurate using a grid?
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By drawing lines from the center of enlargement through points of the original shape to the corresponding points on the enlarged shape.
How does the scale factor affect the enlargement of a triangle with an original base of 2 squares and height of 3 squares when doubled?
The base becomes 4 squares and the height becomes 6 squares with a scale factor of 2.
Describe how a scale factor less than 1 affects the dimensions of a shape during enlargement.
It reduces the dimensions; for example, a scale factor of 1/2 divides each dimension by 2.
What is the role of the center of enlargement in transforming a shape?
The center of enlargement is the point from which the shape is enlarged, determining the position of the enlarged shape.
In the context of enlargements, what does the term 'reverse enlargement' mean?
Finding the original shape's dimensions from the enlarged shape by applying the inverse of the scale factor.
Why is the enlargement of a triangle incorrect if the base and height are multiplied by different factors?
It's incorrect because true enlargement requires that all dimensions are proportionally increased by the same scale factor.
Explain how coordinate axes can be used to perform enlargements.
By marking the center of enlargement on the grid and applying the scale factor to determine transformations.
How is a scale factor of 1/3 applied in reducing a shape's dimensions?
By dividing each dimension of the shape by 3.
What is the key concept that determines how much each length in a shape is multiplied during an enlargement?
Scale Factor
How is the concept of enlargement applied when reducing the size of a shape?
A smaller enlargement still adheres to a scale factor, such as a trapezium base being reduced from 8 to 4 squares with a scale factor of 1/2.
What distinguishes enlargement from other geometric transformations like rotation or reflection?
Enlargement affects size, changing the dimensions proportionally, whereas rotations and reflections do not alter size.
Why must alignment be checked in an enlargement process?
To ensure that all points of the shape are proportionally increased from the center of enlargement.
What practical geometry skills are reinforced by understanding enlargements and transformations?
Skills in map scaling, architectural designs, and understanding spatial transformations.
What rule must be followed to ensure a true enlargement of a shape?
All sides must be multiplied by the same scale factor.
How can you find the scale factor by comparing original and enlarged dimensions?
By identifying the proportion between corresponding dimensions of the original and enlarged shapes.
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