To find the new position of point A after dilation, we can use the formula for dilation. The formula for the coordinates of a point \( (x, y) \) after a dilation centered at \( (h, k) \) with a magnitude of \( r \) is given by:
\[ (x', y') = (h + r \cdot (x - h), k + r \cdot (y - k)) \]
In this problem, we have:
- Point A at \( (0, 0) \)
- Center of dilation at \( (3, 0) \)
- Magnitude of dilation \( r = 3 \)
Using the coordinates of point A and the center of dilation, we can substitute into the formula:
- \( x = 0 \)
- \( y = 0 \)
- \( h = 3 \) (x-coordinate of the center)
- \( k = 0 \) (y-coordinate of the center)
- \( r = 3 \)
Now we calculate the new coordinates:
\[ x' = 3 + 3 \cdot (0 - 3) = 3 + 3 \cdot -3 = 3 - 9 = -6 \]
\[ y' = 0 + 3 \cdot (0 - 0) = 0 + 3 \cdot 0 = 0 \]
So the new ordered pair for point A after dilation is \( (-6, 0) \).
The final answer is:
The new ordered pair would be at (-6, 0).
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