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Graph the image of △FGH after a dilation with a scale factor of 2, centered at the origin.


To solve this problem, we need to apply a dilation with a scale factor of 2, centered at the origin, to the vertices of triangle \( \Delta FGH \).

1. **Original coordinates**:
   - \( F(-4, 4) \)
   - \( G(4, 4) \)
   - \( H(0, -4) \)

2. **Dilating each point by a factor of 2**:
   For dilation centered at the origin, each coordinate of a point is multiplied by the scale factor.

   - \( F' = (-4 \times 2, 4 \times 2) = (-8, 8) \)
   - \( G' = (4 \times 2, 4 \times 2) = (8, 8) \)
   - \( H' = (0 \times 2, -4 \times 2) = (0, -8) \)

3. **New coordinates after dilation**:
   - \( F'(-8, 8) \)
   - \( G'(8, 8) \)
   - \( H'(0, -8) \)

To graph the dilated triangle, you would plot the new points \( F'(-8, 8) \), \( G'(8, 8) \), and \( H'(0, -8) \) on the graph and connect them to form the new image of triangle \( \Delta FGH \).

Would you like further details or assistance in graphing this?

Here are 5 related questions:
1. How do you determine the center of dilation in any transformation?
2. What happens to the size of a shape after a dilation with a scale factor greater than 1?
3. How do you apply a dilation to shapes not centered at the origin?
4. Can you describe the difference between dilation and translation?
5. How would a dilation with a fractional scale factor affect the triangle?

**Tip**: When performing dilations, always multiply both the x- and y-coordinates of each point by the scale factor to get the image coordinates.

Graph the image of △FGH after a dilation with a scale factor of 2, centered at the origin.

Learn how to graph the dilated image of triangle FGH on a coordinate plane with a scale factor of 2, centered at the origin. This guide includes a step-by-step explanation of applying dilation transformations, suitable for Grade 8 geometry students.

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