Describing Dilations | Worksheet - Free Printable

Looking at Problem 4, I can see two trapezoids: a smaller orange trapezoid (preimage) and a larger green trapezoid (dilated image).

To find the scale factor, I need to compare corresponding side lengths or distances from the origin.

Let me examine the coordinates of the vertices:
- Preimage trapezoid (smaller, orange): Let's call it WXYZ with W(2,1), X(4,1), Y(3,-1), Z(1,-1)
- Dilated image trapezoid (larger, green): Let's call it W'X'Y'Z' with W'(6,3), X'(12,3), Y'(9,-3), Z'(3,-3)

I can calculate the scale factor by comparing corresponding points. Let's use point W(2,1) and W'(6,3):
- The x-coordinate changed from 2 to 6 (multiplied by 3)
- The y-coordinate changed from 1 to 3 (multiplied by 3)

Let me verify with another point, X(4,1) and X'(12,3):
- The x-coordinate changed from 4 to 12 (multiplied by 3)
- The y-coordinate changed from 1 to 3 (multiplied by 3)

And for point Y(3,-1) and Y'(9,-3):
- The x-coordinate changed from 3 to 9 (multiplied by 3)
- The y-coordinate changed from -1 to -3 (multiplied by 3)

And for point Z(1,-1) and Z'(3,-3):
- The x-coordinate changed from 1 to 3 (multiplied by 3)
- The y-coordinate changed from -1 to -3 (multiplied by 3)

All coordinates are multiplied by 3, so the scale factor is 3.

Therefore, trapezoid WXYZ was dilated by a scale factor of 3 to form trapezoid W'X'Y'Z'.

Now I have all the information needed to complete the task.

Final Answer:

Here are the descriptions for each dilation:

Problem 2: Square ABCD was dilated by a scale factor of 4 to form square A'B'C'D'.

Problem 3: Triangle EFG was dilated by a scale factor of 3 to form triangle E'F'G'.

Problem 4: Trapezoid WXYZ was dilated by a scale factor of 3 to form trapezoid W'X'Y'Z'.