To find the coordinates of a dilation of a point (1, 2) by a factor of 0.5, follow these steps:
1. Understand the Dilation Transformation:
Dilation involves scaling the coordinates of a point by a given factor. If the original point has coordinates [tex]\((x, y)\)[/tex], and we apply a dilation with a scale factor [tex]\(k\)[/tex], the new coordinates will be [tex]\((kx, ky)\)[/tex].
2. Identify the Original Coordinates and Scale Factor:
The original coordinates are [tex]\((1, 2)\)[/tex], and the scale factor [tex]\(k\)[/tex] is 0.5.
3. Apply the Scale Factor to Each Coordinate:
- For the x-coordinate: Multiply the original x-coordinate by the scale factor.
[tex]\[
x_{\text{dilated}} = k \cdot x_{\text{original}} = 0.5 \cdot 1 = 0.5
\][/tex]
- For the y-coordinate: Multiply the original y-coordinate by the scale factor.
[tex]\[
y_{\text{dilated}} = k \cdot y_{\text{original}} = 0.5 \cdot 2 = 1
\][/tex]
4. Determine the New Coordinates:
After applying the dilation, the new coordinates are [tex]\((0.5, 1)\)[/tex].
Therefore, the coordinates of the dilation of the point [tex]\((1, 2)\)[/tex] by a factor of 0.5 are [tex]\((0.5, 1)\)[/tex].
