Math 2 Unit 2
SIZE
TRANSFORMATIONS
|
This lesson will help you see:
1) The effects of size transformations on length, slope, and
area for various shapes.
2) The concepts associated with size transformations and similarity
for plane shapes. |
| What
is a Size Transformation???
A
size transformation is actually changing the size of an object
by multiplying or dividing the coordinates by a specific factor.
Example:
(x,y)-->(2x,2y)
(5,5)-->(2x5, 2x5) or (10,10) |
Length
of a side= 5
Area=
25
|
Length
of a side= 10
Area=
100 |
L1=
Small Square
L2=
Large Square
|
| Here,
your second point (2x,2y) is two times as large as your first
point (x,y). Also, the area of the shape above increases by
a multiple of 4 (the size factor increased by 2 on each side).
If the length was multiplied by a factor of 3, then the area
would increase by a factor of 3 on each side or 9 because you
multiply them. The slope remains the same in the size transformation
because the shape remains the same. Only the size and area change. |
| ANOTHER
EXAMPLE: |
|
|
In
the example to the left, you can see that when transforming
an image by a factor of 2, you simply multiply all of the
points by that factor.
Here
the shape doubles in size and quadruples in area. Again, the
slope remains constant in both images. |
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