Exploring Dilation

Exploring dilation:

In this activity you will explore how the image changes when performing dilations.[br]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.[br]Compare the pre-image and the image.[br]What happens to the image?

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

2) When k = 1

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

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

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?

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

4) Finding the scale factor

Slide k to any value.[br]Calculate each of the values: [math]\frac{OA'}{OA},\frac{OB'}{OB},\frac{A'B'}{AB}[/math][br]What do you notice about all of them?

5) Finding the scale factor, k, using ordered pairs

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

6) Finding ordered pairs using the scale factor, k

Using your response from question 5, what would the coordinates of A' and B' be if k = 5?

A'(2, 5), B'(2, 10) A'(5, 2), B'(10, 2) A'(6, 8), B'(7, 7) A'(5, 10), B'(10, 10)

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

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

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