Exploring Dilation

Exploring dilation:

In this activity you will explore how the image changes when performing dilations. Follow the instructions given for each question and select/enter the associated properties of dilation.

1) When 0 < k < 1

Slide k to any value between 0 and 1, for example k = 0.5. Compare the pre-image and the image. What happens to the image?

Select all that apply

A
It shrinks, becomes smaller than the pre-image.
B
It enlarges, becomes bigger than the pre-image.
C
It stays the same, nothing changes.
D
The image disappears.

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2) When k = 1

Set the slider to k = 1. Compare the pre-image and the image. What do you notice?

Select all that apply

A
It shrinks, becomes smaller than the pre-image.
B
It enlarges, becomes bigger than the pre-image.
C
It stays the same, the size of the image and the pre-image are the equal.
D
The image disappears.

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3) When k > 1

Slide k to any value greater than 1, for example k = 1.5. Compare the pre-image and the image. What happens to the image?

Select all that apply

A
It shrinks, becomes smaller than the pre-image.
B
It enlarges, becomes bigger than the pre-image.
C
It stays the same, the size of the image and the pre-image are the equal.
D
The image disappears.

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4) Finding the scale factor

Slide k to any value. Calculate each of the values: What do you notice about all of them?

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5) Finding scale factor, k, using ordered pairs

Slide k to 2. Note the coordinates of A, B, A', and B'. How can you find the scale factor using the ordered pairs?

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6) Comparing corresponding segments of the image and pre-image

Set k = 2 and calculate the slopes of segments AB and A'B'. What do the values of the slopes tell you?

Select all that apply

A
The slopes are the same, so the segments are parallel.
B
The slopes are opposite reciprocals, so the segments are perpendicular.
C
The slopes are not the same nor opposite reciprocals, so the segments will intersect.

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Exploring Dilation