Dilations Part 3: What Do You Notice?

In this app below, points A and B are dilated about point O. Their images are A' and B', respectively. Interact with this app for a few minutes. Then, answer the questions that follow.

Move A to (1,2) and move B to (-3,4). Dilate A and B about O with a scale factor of 2. What are the coordinates (x,y) of their images (A' and B')?

Move A to (1,2) and move B to (-3,4). Dilate A and B about O with a scale factor of 3. What are the coordinates (x,y) of their images (A' and B')?

Move A to (1,2) and move B to (-3,4). Dilate A and B about O with a scale factor of 0.5. What are the coordinates (x,y) of their images (A' and B')?

Move A to (1,2) and move B to (-3,4). Dilate A and B about O with a scale factor of -1. What are the coordinates (x,y) of their images (A' and B')?

Move A to (1,2) and move B to (-3,4). Dilate A and B about O with a scale factor of -2. What are the coordinates (x,y) of their images (A' and B')?

Move A to (1,2) and move B to (-3,4). Dilate A and B about O with a scale factor of -0.5. What are the coordinates (x,y) of their images (A' and B')?

Suppose a point [math]A\left(x,y\right)[/math] is dilated about the origin [math]O\left(0,0\right)[/math] by a scale factor [math]k[/math]. What are the coordinates [math]\left(x,y\right)[/math]of its image [math]A'[/math]?

[math]\left(k\cdot x,k\cdot y\right)[/math] All of the above [math]\left(x,y\right)[/math] None of the above [math]\left(k\cdot y,k\cdot x\right)[/math]

Dilations Part 3: What Do You Notice?

In this app below, points A and B are dilated about point O. Their images are A' and B', respectively. Interact with this app for a few minutes. Then, answer the questions that follow.

Information: Dilations Part 3: What Do You Notice?