Question

d=( 0,2)
Suppose you dilate the rectangle on the coordinate plane using a magnitude of 1/2 and the center of dilation at (1,1) . What would be the corresponding ordered pair to the current point D ?

Answer 1

To find the new coordinates of point D (0, 2) after a dilation centered at (1, 1) with a scale factor of \( \frac{1}{2} \), you can follow these steps:

1. **Determine the vector from the center of dilation to point D**:
\[
\text{Vector} = (0 - 1, 2 - 1) = (-1, 1)
\]

2. **Dilate this vector by the scale factor \( \frac{1}{2} \)**:
\[
\text{Dilated Vector} = \left(-1 \cdot \frac{1}{2}, 1 \cdot \frac{1}{2}\right) = \left(-\frac{1}{2}, \frac{1}{2}\right)
\]

3. **Add this dilated vector to the center of dilation (1, 1)**:
\[
\text{New Point} = (1 + -\frac{1}{2}, 1 + \frac{1}{2}) = \left(1 - \frac{1}{2}, 1 + \frac{1}{2}\right) = \left(\frac{1}{2}, \frac{3}{2}\right)
\]

So, the corresponding ordered pair to the current point D (0, 2) after dilation is \(\left(\frac{1}{2}, \frac{3}{2}\right)\).