https://file.aiquickdraw.com/mathbot/file/1726624091748gbiil3ih.jpg

The task in this image involves dilating triangle \(DEF\) with a scale factor of 2 and a center of dilation at point \(Q\). The goal is to determine the relationship between the distances of the points of triangle \(DEF\) from the center of dilation before and after the dilation.

For this problem, the key steps are:

1. **Determine the original distance from the center of dilation** (point \(Q\)) to each point of the triangle \(DEF\).
2. **Apply the scale factor** of 2. Since dilation involves multiplying the distance of each point from the center by the scale factor, each point should end up twice as far from point \(Q\) as it was originally.
3. **Calculate the new distance** of each dilated point from point \(Q\).

In the image, for point \(D\), the distance from \(Q\) is given as 5 units. Using the formula:

\[
\text{New distance} = \text{Original distance} \times \text{Scale factor}
\]

For point \(D\), this becomes:

\[
\text{New distance} = 5 \times 2 = 10
\]

Would you like further details or have any questions on how to proceed? Here are five related questions to explore further:

1. How does dilation affect the angles of triangle \(DEF\)?
2. What is the general formula for dilating a point on a coordinate plane?
3. What happens if the scale factor is less than 1?
4. How would the triangle change if the center of dilation was outside the triangle?
5. Can you describe the impact of dilation on the area of the triangle?

**Tip:** Dilation changes distances but preserves the shape and angles of geometric figures.

Dilate triangle DEF with a scale factor of 2 and center of dilation at point Q. Record the scale factor and calculate the corresponding points' distances from the center of dilation.

Explore how to dilate triangle DEF with a scale factor of 2, using point Q as the center of dilation. Learn the concept of dilation, apply the formula for scale factor, and calculate the new distances from the center of dilation. Suitable for Grades 8-10 geometry students.

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