# Dilation Exploration

## DIRECTIONS:

**k**. Set Min = -5, Max = 5, Increment = 0.1 2) Select the DILATE FROM POINT tool. Highlight a box around

**point**,

*A***point**, and

*B***Curious George's picture**. Then select point

*C*(to serve as center of dilation) In the pop-up box that appears, enter "k" (without the " " 's) to serve as the scale factor. 3) Select the Move tool.

**Explore!**Please answer the questions that appear below the applet.

## 1)

Suppose **point A = (1, 2)** is dilated about

**C(0,0)**with scale factor 2. Suppose

**point**is dilated about

*B*= (4, 1)**C(0,0)**with scale factor 2. What would the coordinates of the

*A'*= image of

*A*be? What would the coordinates of

*B' =*image of

*B*be?

## 2)

Suppose **point A = (1, 2)** is dilated about

**C(0,0)**with scale factor 3. Suppose

**point**is dilated about

*B*= (4, 1)**C(0,0)**with scale factor 3. What would the coordinates of the

*A'*= image of

*A*be? What would the coordinates of

*B' =*image of

*B*be?

## 3)

Suppose **point A = (1, 2)** is dilated about

**C(0,0)**with scale factor 4. Suppose

**point**is dilated about

*B*= (4, 1)**C(0,0)**with scale factor 4. What would the coordinates of the

*A'*= image of

*A*be? What would the coordinates of

*B' =*image of

*B*be?

## 4)

Suppose **point A = (1, 2)** is dilated about

**C(0,0)**with scale factor 0.5. Suppose

**point**is dilated about

*B*= (4, 1)**C(0,0)**with scale factor 0.5. What would the coordinates of the

*A'*= image of

*A*be? What would the coordinates of

*B' =*image of

*B*be?

## 5)

Suppose **point A = (1, 2)** is dilated about

**C(0,0)**with scale factor 0. Suppose

**point**is dilated about

*B*= (4, 1)**C(0,0)**with scale factor 0. What would the coordinates of the

*A'*= image of

*A*be? What would the coordinates of

*B' =*image of

*B*be?

## 5)

Suppose **point A = (1, 2)** is dilated about

**C(0,0)**with scale factor -1. Suppose

**point**is dilated about

*B*= (4, 1)**C(0,0)**with scale factor -1. What would the coordinates of the

*A'*= image of

*A*be? What would the coordinates of

*B' =*image of

*B*be? What if the scale factor was -2? -3?

## 5)

What do you notice? Write any observation(s) you have below.

## 6)

Notice how the image of **f **is called **f'**.
How do their lengths compare?
**When is f' bigger than f?
When is it smaller than f? **
*Be specific! *

## 7)

Go to the STEPS window now (notebook-looking icon to the left of the circle/triangle symbol)
Hide the pictures of George and his image by de-selecting the bubbles of** pic1** & **pic1'.**
This should only leave the points and segments remaining.
What else can we conclude segments about f' and f? *Be sure to move points A and B around! *

## 8)

Use the tool(s) provided to you to prove your conjecture for (7) is true. Can you also illustrate this another way?