To find the corresponding ordered pair for the point D(3, 3) after performing a dilation with a center of dilation at (1, 1) and a scale factor of \( \frac{1}{2} \), you can use the following formula for dilation:
\[ (x', y') = \left( x_c + k(x - x_c), y_c + k(y - y_c) \right) \]
Where:
- \((x', y')\) is the new point after dilation,
- \((x_c, y_c)\) is the center of dilation,
- \(k\) is the scale factor,
- \((x, y)\) is the original point.
Substituting the known values:
- Center of dilation \((x_c, y_c) = (1, 1)\)
- Original point \(D = (3, 3)\)
- Scale factor \(k = \frac{1}{2}\)
Now, plug these values into the formula:
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For the x-coordinate: \[ x' = 1 + \frac{1}{2}(3 - 1) = 1 + \frac{1}{2}(2) = 1 + 1 = 2 \]
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For the y-coordinate: \[ y' = 1 + \frac{1}{2}(3 - 1) = 1 + \frac{1}{2}(2) = 1 + 1 = 2 \]
So, the new coordinates after dilation will be: \[ (2, 2) \]
Thus, the corresponding ordered pair to the current point D(3, 3) after the dilation is \((2, 2)\).
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