Question

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 ? (1 point)
D is 3,3

Answer 1

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:

1. For the x-coordinate:
\[
x' = 1 + \frac{1}{2}(3 - 1) = 1 + \frac{1}{2}(2) = 1 + 1 = 2
\]

2. 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 \((2, 2)\).