To find the coordinates of the new vertex \( D' \) after reducing the triangle with a scale factor of \( \frac{1}{2} \) and using the center of dilation at (0, 0), you'll need the original coordinates of vertex \( D \). Since this information is not provided, I'll explain the general process.
Let's assume the original coordinates of vertex \( D \) are \( (x, y) \). When we apply a scale factor of \( \frac{1}{2} \) with the center of dilation at (0, 0), the new coordinates \( D' \) can be calculated as follows:
\[ D' = \left( \frac{1}{2} x, \frac{1}{2} y \right) \]
However, we need to select from the given options. Without the original coordinates of \( D \), it's difficult to verify exactly the new coordinates. If this problem is based on a graphical representation whose vertices were reduced and mapped, then you should consider the list of given options:
1. (-2.5, 0)
2. (0, 2.5)
3. (0, -2.5)
4. (-2.5, -5)
Let's analyze each option considering the scaling factor being \( \frac{1}{2} \):
- If the original coordinates of \( D \) were (-5, 0), scaling by \( \frac{1}{2} \) gives \( D' = \left(\frac{1}{2} \cdot -5, \frac{1}{2} \cdot 0 \right) = (-2.5, 0) \).
- If the original coordinates of \( D \) were (0, 5), scaling by \( \frac{1}{2} \) gives \( D' = \left( \frac{1}{2} \cdot 0, \frac{1}{2} \cdot 5 \right) = (0, 2.5) \).
- If the original coordinates of \( D \) were (0, -5), scaling by \( \frac{1}{2} \) gives \( D' = \left( \frac{1}{2} \cdot 0, \frac{1}{2} \cdot -5 \right) = (0, -2.5) \).
- If the original coordinates of \( D \) were (-5, -10), scaling by \( \frac{1}{2} \) gives \( D' = \left( \frac{1}{2} \cdot -5, \frac{1}{2} \cdot -10 \right) = (-2.5, -5) \).
Since these options should correspond to transformations due to scaling, and without the original vertex \( D \) coordinates, the interpretation is ambiguous. However, all given options correspond to valid possibilities of transformed coordinates from vertices scaled \( \frac{1}{2} \) from specific candidate original coordinates.
If you have the original coordinates of \( D \), you can substitute them in the calculation to confirm the exact new position \( D' \).
12. Triangle FDP is reduced with a scale factor of ½ and a center of (0, 0). Find the coordinates of the new coordinates of the vertex, D’ (__, __):
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Captionless Image
(-2.5, 0)
(0, 2.5)
(0, -2.5)
(-2.5, -5)
1 answer