To find the coordinates of the new vertex \( P' \) of triangle FDP after it has been reduced by a scale factor of \( \frac{1}{2} \) with respect to the center at \( (0, 0) \), you take the coordinates of vertex \( P \) (let's assume the original coordinates of \( P \) are \( (x_P, y_P) \)) and apply the scale transformation.
The formula to find the new coordinates after scaling is given by:
\[ P' = \left( x_P \cdot \text{scale factor}, y_P \cdot \text{scale factor} \right) \]
Substituting the scale factor of \( \frac{1}{2} \):
\[ P' = \left( x_P \cdot \frac{1}{2}, y_P \cdot \frac{1}{2} \right) \]
This means you simply multiply both the x and y coordinates of point \( P \) by \( \frac{1}{2} \).
For example, if the original coordinates of \( P \) are \( (4, 6) \), then the new coordinates \( P' \) will be:
\[ P' = \left( 4 \cdot \frac{1}{2}, 6 \cdot \frac{1}{2} \right) = (2, 3) \]
To find the specific coordinates for vertex \( P' \), simply apply this process using the actual coordinates of vertex \( P \). If you provide the coordinates of \( P \), I can give you the exact coordinates of \( P' \).