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April 10, 2023
Enlargement
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1. Enlargement.
April 10, 2023
Look at this ZebraHere is another.It is exactly the same shape, but twice the size.
In fact, the bigger zebra is an enlargement of the smaller picture.It has been enlarged by a scale factor of 2.
Explanation
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April 10, 2023
Here is a polygon drawn onto 1cm square paper.
If you make a 2 times enlargement, that is to say enlarge it by a scale factor of 2 it looks like this.You can see that each side is twice the length by counting the squares form one end to the other.
one down, one along
two down, two along
one down, three along
two down, six along
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Here are two polygons, one an enlargement of the other.
April 10, 2023
Here are two polygons, one an enlargement of the other.Place them on a Cartesian plane.
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April 10, 2023
Here are two polygons, one an enlargement of the other.Place them on a Cartesian plane.
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Notice that you can join up points in the same place on each shape.
Extend the lines beyond the smaller polygon.They meet at point (0,0), also known as the origin. (0,0) is therefore the centre of enlargement.
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April 10, 2023
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This is the length from the centre of enlargement to a point on the original.It is twice this length from the centre of enlargement to the corresponding point on the enlarged polygon.This is the case for all corresponding points.
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April 10, 2023
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As the centre of enlargement is at the origin, (0,0), each coordinate point on the original can be multiplied by the scale factor to find the corresponding point on the enlargement.
× 2 becomes(3,2) (6,4)(5,2) (10,4)(6,3) (12,6)(3,3) (6,6)
Here, the scale factor is 2.
The scale factor is sometimes called k.
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April 10, 2023
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The centre of enlargement can be inside the original shape.
“Enlarge this shape by scale factor 3, centre the point A.”
A
Measure one length from A to a point on the polygon.Another equal length makes 2.A third equal length takes you to where the corresponding point will be on the enlargement.
1 length2 lengths3
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April 10, 2023
When you describe an enlargement, you must give the scale factor and the centre of enlargement.An enlargement is a type of transformation.
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April 10, 2023
When you describe an enlargement, you must give the scale factor and the centre of enlargement.An enlargement is a type of transformation.
“Describe the transformation that maps shape C onto shape D”
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“An enlargement by scale factor 3, centre the point (5,2).”
C
D
Join three sets of corresponding points.
Explanation
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