What is the image of left parenthesis, minus, 8, comma, 8, right parenthesis(−8,8) after a dilation by a scale factor of one quarter 
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  centered at the origin?

The point you are working with is \((-8, 8)\), and the scale factor for the dilation is \(\frac{1}{4}\). Since the dilation is centered at the origin, you can apply the scale factor directly to both the \(x\)- and \(y\)-coordinates of the point.

### Step-by-step process:
1. **Start with the point \((-8, 8)\).**
2. **Apply the scale factor \(\frac{1}{4}\) to each coordinate:**
   - For the \(x\)-coordinate: \(-8 \times \frac{1}{4} = -2\)
   - For the \(y\)-coordinate: \(8 \times \frac{1}{4} = 2\)

Thus, after the dilation, the image of the point \((-8, 8)\) is:

\[
(-2, 2)
\]

Would you like any further details on this process, or do you have any questions?

Here are 5 related questions to consider:
1. How do you find the image of a point after dilation with a different center?
2. What happens to a point when it is dilated by a factor greater than 1?
3. How do you calculate dilations in higher dimensions, such as 3D space?
4. How does dilation affect the distance between two points?
5. How do you reverse a dilation (find the pre-image of a point)?

**Tip:** When applying dilations, always remember that the distance from the center of dilation changes by the scale factor, but the direction remains the same.

What is the image of left parenthesis, minus, 8, comma, 8, right parenthesis (−8,8) after a dilation by a scale factor of one quarter centered at the origin?

Learn how to find the image of the point (-8, 8) after a dilation by a scale factor of 1/4 centered at the origin. This problem covers key geometric concepts, including dilation and transformations. Suitable for students in Grades 8-10.

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