https://file.aiquickdraw.com/mathbot/file/1726150179527yo0uea8b.jpg

To determine the scale factor of the dilation between the trapezoids \(WXYZ\) and \(W'X'Y'Z'\), we need to compare the distances between corresponding points or sides.

### Step-by-step process:

1. **Identify corresponding points**:
   - The corresponding points of the two trapezoids are \( W \leftrightarrow W' \), \( X \leftrightarrow X' \), \( Y \leftrightarrow Y' \), and \( Z \leftrightarrow Z' \).

2. **Measure distance between corresponding points**:
   - Let's find the coordinates of the vertices of trapezoid \(WXYZ\) (larger trapezoid):
     - \( W(8, -2) \), \( X(8, 6) \), \( Y(-6, 6) \), \( Z(-6, -8) \).
   - Now the coordinates of the corresponding points of the dilated trapezoid \(W'X'Y'Z'\):
     - \( W'(4, -1) \), \( X'(4, 3) \), \( Y'(-2, 3) \), \( Z'(-2, -4) \).

3. **Calculate distances**:
   - For simplicity, we will measure the distance between \(W\) and \(W'\), as well as between \(Z\) and \(Z'\), to find the scale factor.
   - Distance from \(W\) to the origin: \(W(8, -2)\), so its distance from the origin is \( \sqrt{8^2 + (-2)^2} = \sqrt{64 + 4} = \sqrt{68} \).
   - Distance from \(W'\) to the origin: \(W'(4, -1)\), so its distance from the origin is \( \sqrt{4^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17} \).

4. **Find scale factor**:
   - The scale factor is the ratio of the distances from the center of dilation (which we assume is the origin):
   \[
   \text{Scale factor} = \frac{\text{Distance from origin to } W'}{\text{Distance from origin to } W} = \frac{\sqrt{17}}{\sqrt{68}} = \frac{1}{2}.
   \]

Thus, the scale factor of the dilation is \( \boxed{\frac{1}{2}} \).

Would you like more details or have any questions?

---

Here are 5 related questions for further exploration:
1. How would the trapezoid's area change if the scale factor was 3 instead of \(\frac{1}{2}\)?
2. What is the general formula for the scale factor in dilations centered at the origin?
3. How can you determine the center of dilation if it's not given?
4. How does the perimeter of a figure change after dilation?
5. Can the scale factor be negative, and what would that imply geometrically?

**Tip:** When finding the scale factor in dilation, always ensure to use the distance between corresponding points, and make sure the center of dilation is clear (often the origin).

The trapezoid W'X'Y'Z' is a dilation of the trapezoid WXYZ. What is the scale factor of the dilation?

Learn how to find the scale factor of dilation between trapezoids WXYZ and W'X'Y'Z'. This problem involves calculating the distances between corresponding points and applying the formula for scale factor. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation