1. Find a point on the ray whose distance from is twice the distance from to and label it .
2. Find a point on the ray whose distance from is half the distance from to and label it .

Here is a diagram that shows 9 points.

Nine points. Points E, F, G and H are mostly horizontal, spread out evenly and form a line. Point A above F, and point B above G, point H and Point I below and to the right also form a line. Point F, point D, point B and point C far above between point G and H also form a line.

1. Dilate using a scale factor of 5 and as the center of dilation. Which point is its image?
2. Using as the center of dilation, dilate so that its image is . What scale factor did you use?
3. Using as the center of dilation, dilate so that its image is . What scale factor did you use?
4. To dilate so that its image is , what point on the diagram can you use as the center of dilation?
5. Dilate using as the center of dilation and a scale factor of . Which point is its image?
6. Describe a dilation that uses a labeled point as its center of dilation and that would take to .
7. Using as the center of dilation, dilate so that its image is itself. What scale factor did you use?

1. Draw the images of points and using as the center of dilation and a scale factor of 4. Label the new points and .

   

2. Draw the images of points and  using as the center of dilation and a scale factor of . Label the new points and .

   
   Pause here so your teacher can review your diagram. Your teacher will then give you a scale factor to use in the next part.

3. Let's make a perspective drawing. Here is a rectangle.

   

   1. Choose a point inside the shaded circular region but outside the rectangle to use as the center of dilation. Label it .

   2. Use your center and the scale factor you were given to draw the image under the dilation of each vertex of the rectangle, one at a time. Connect the dilated vertices to create the dilated rectangle.

   3. Draw segments that connects each of the original vertices with its image. This will make your diagram look like a cool three-dimensional drawing of a box! If time allows, you can shade the sides of the box to make it look more realistic.

   4. Compare your drawing to other people’s drawings. What is the same and what is different? How do the choices you made affect the final drawing? Was your dilated rectangle closer to than to the original rectangle, or farther away? How is that decided?