The pink figure is a dilation image of the black figure. The labeled point is the center of dilation. Tell whether the dilation is an enlargement or a reduction. Then find the scale factor of the dilation.
L
An array of dots has 9 columns and 9 rows of dots. In the bottom row, the middle dot is labeled "L." A black polygon has 10 sides that connect the following vertices, where point L is taken to be the origin and coordinates are in terms of dots: (negative 4, 0); (negative 4, 6); (negative 2, 6); (negative 2, 8); (0, 8); (0, 6); (2, 6); (2, 2); (4, 2); (4, 0). A pink polygon has 10 sides that connect the following vertices, where point L is taken to be the origin and coordinates are in terms of dots: (negative 2, 0); (negative 2, 3); (negative 1, 3); (negative 1, 4); (0, 4); (0, 3); (1, 3); (1, 1); (2, 1); (2, 0).
The dilation is a reduction because the pink figure is smaller than the black figure.
To find the scale factor of the dilation, we can compare the corresponding side lengths.
Let's compare the length of a side of the black polygon to the corresponding side of the pink polygon.
For the black polygon:
- Side length from (-4,0) to (-4,6) is 6 dots
- Side length from (-4,6) to (-2,6) is 2 dots
- Side length from (-2,6) to (-2,8) is 2 dots
- Side length from (-2,8) to (0,8) is 2 dots
- Side length from (0,8) to (0,6) is 2 dots
- Side length from (0,6) to (2,6) is 2 dots
- Side length from (2,6) to (2,2) is 4 dots
- Side length from (2,2) to (4,2) is 2 dots
- Side length from (4,2) to (4,0) is 2 dots
For the pink polygon:
- Side length from (-2,0) to (-2,3) is 3 dots
- Side length from (-2,3) to (-1,3) is 1 dot
- Side length from (-1,3) to (-1,4) is 1 dot
- Side length from (-1,4) to (0,4) is 1 dot
- Side length from (0,4) to (0,3) is 1 dot
- Side length from (0,3) to (1,3) is 1 dot
- Side length from (1,3) to (1,1) is 2 dots
- Side length from (1,1) to (2,1) is 1 dot
- Side length from (2,1) to (2,0) is 1 dot
The corresponding side lengths are proportional with a scale factor of 2. Therefore, the scale factor of the dilation is 2.
wrong
I apologize for the mistake. Let's try again.
To find the scale factor of the dilation, we can compare the distance of a point on the black figure to the center of dilation (point L) and the corresponding point on the pink figure to the center of dilation.
For example, let's compare the point (-4,0) on the black figure to the point (-2,0) on the pink figure.
The distance from point L (-2,0) to point (-4,0) is 2 dots.
The distance from point L to the corresponding point on the pink figure (-2,0) is also 2 dots.
Therefore, the scale factor of the dilation is 1, indicating that there is no dilation - the pink figure has the same size as the black figure but is just a different shape due to the transformation.