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To perform a dilation with a scale factor of 5 about the origin for the given points \( Y(1, -1) \), \( X(0, 1) \), and \( W(1, 1) \), we multiply each coordinate by 5.

The formula for dilation about the origin with scale factor \( k \) is:
\[
(x', y') = (k \cdot x, k \cdot y)
\]
where \( k = 5 \).

Now, let's calculate the new coordinates for each point:

1. **For \( Y(1, -1) \)**:
   \[
   Y'(x', y') = (5 \cdot 1, 5 \cdot (-1)) = (5, -5)
   \]

2. **For \( X(0, 1) \)**:
   \[
   X'(x', y') = (5 \cdot 0, 5 \cdot 1) = (0, 5)
   \]

3. **For \( W(1, 1) \)**:
   \[
   W'(x', y') = (5 \cdot 1, 5 \cdot 1) = (5, 5)
   \]

Thus, the new points after dilation are:
- \( Y'(5, -5) \)
- \( X'(0, 5) \)
- \( W'(5, 5) \)

Would you like more details or have any questions?

Here are some related questions you might find useful:

1. What is the general formula for dilation about a point other than the origin?
2. How does dilation affect the distance between two points?
3. How does dilation with a factor less than 1 change the shape?
4. Can you perform a dilation with a negative scale factor?
5. How do you combine transformations, such as dilation and rotation?

**Tip**: When dilating a figure, all points move along straight lines from the center of dilation, and their distances from the center increase (or decrease) by the scale factor.

Dilation of 5 about the origin for the points Y(1, -1), X(0, 1), W(1, 1)

Perform a dilation with a scale factor of 5 about the origin for the points Y(1, -1), X(0, 1), and W(1, 1). This step-by-step solution includes the dilation formula and application to coordinate geometry, suitable for Grades 9-12.

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