11. 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, P’ (__, __):

Question

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Captionless Image
(-3 ,0)
(0 , -3)
(3, 0)
(3, 3)

Answer 1

To find the coordinates of the new vertex \( P' \) after the triangle FDP is reduced with a scale factor of \( \frac{1}{2} \) and a center of (0, 0), follow these steps:

1. **Determine the original coordinates of \( P \)**: Given in the problem, let's denote the coordinates of \( P \) as \((x, y)\).

2. **Apply the scale factor**: Multiply both coordinates of \( P \) by the scale factor \( \frac{1}{2} \).

3. **Coordinates of \( P' \)**: If the coordinates of \( P \) are \((x, y)\), then the new coordinates \( P' \) after applying the scale factor will be:
\[
P' = \left( \frac{x}{2}, \frac{y}{2} \right)
\]

Now, let's consider the given choices to find the original vertex \( P \).

- If the original \( P \) is \((-3, 0)\):
\[
P' = \left( \frac{-3}{2}, \frac{0}{2} \right) = \left( -\frac{3}{2}, 0 \right)
\]
This choice does not fit the options provided.

- If the original \( P \) is \((0, -3)\):
\[
P' = \left( \frac{0}{2}, \frac{-3}{2} \right) = \left( 0, -\frac{3}{2} \right)
\]
This choice also does not fit the options provided.

- If the original \( P \) is \((3, 0)\):
\[
P' = \left( \frac{3}{2}, \frac{0}{2} \right) = \left( \frac{3}{2}, 0 \right)
\]
This choice also does not fit the options provided.

- If the original \( P \) is \((3, 3)\):
\[
P' = \left( \frac{3}{2}, \frac{3}{2} \right) = \left( \frac{3}{2}, \frac{3}{2} \right)
\]
This choice also does not fit the options provided.

Since none of the provided vertex coordinates work with the transformation of a scale factor of \(\frac{1}{2}\), let's ensure we understand the problem correctly. Given the choices, here they do not conform to the mathematical transformation. Verify if there were specific notation or problem details not shown here.

If any inconsistencies persist in the transformation or vertices provided, double-check the problem, as some new data or rechecking the information might be necessary.