What is the scale factor of dilation if the points have went from (-1,2), (-4,-2), and (4,-4) to (-2,4), (-8,-4), and (8,-8)? Is this a reduction or enlargement?
To find the scale factor of dilation, we can calculate the ratio of the lengths of corresponding sides or the ratio of the distances from the center of dilation.
The distance between the point (-1, 2) and the origin (center of dilation) is sqrt((-1)^2 + 2^2) = sqrt(5).
The distance between the point (-2, 4) and the origin is sqrt((-2)^2 + 4^2) = sqrt(20) = 2sqrt(5).
Therefore, the scale factor of dilation is 2sqrt(5) / sqrt(5) = 2.
Since the scale factor is greater than 1, this is an enlargement.
To find the scale factor of dilation, we can compare the distances between corresponding points of the pre-image (original) and the image (transformed).
Let's take one pair of points: (-1, 2) and (-2, 4).
- The x-coordinate has changed from -1 to -2. The difference is -2 - (-1) = -1.
- The y-coordinate has changed from 2 to 4. The difference is 4 - 2 = 2.
Now, let's calculate the scale factor of the x-coordinate:
-1 / -2 = 0.5
And the scale factor of the y-coordinate:
2 / 4 = 0.5
Since both scale factors are equal (0.5), the scale factor of dilation is 0.5.
Now, let's check if it's a reduction or enlargement based on the scale factor.
If the scale factor is less than 1, it means the image is smaller than the original, and therefore, it is a reduction.
In this case, the scale factor is 0.5, which is less than 1. So, the transformation is a reduction.
To find the scale factor of dilation, we can use the formula:
Scale factor = ratio of corresponding side lengths or distances between the corresponding points
In this case, let's consider the distance between the first set of corresponding points and the second set of corresponding points.
The distance between the points (-1,2) and (-2,4) is sqrt(((-1)-(-2))^2 + ((2)-(4))^2) = sqrt(1 + 4) = sqrt(5).
Similarly, the distance between (-4,-2) and (-8,-4) is sqrt(((-4)-(-8))^2 + ((-2)-(-4))^2) = sqrt(16 + 4) = sqrt(20).
And the distance between (4,-4) and (8,-8) is sqrt(((4)-(8))^2 + ((-4)-(-8))^2) = sqrt(16 + 16) = sqrt(32).
Now, let's calculate the scale factor:
Scale factor = (sqrt(5)) / (sqrt(20)) = (sqrt(5)) / (2 * sqrt(5)) = 1 / 2
Therefore, the scale factor of dilation is 1/2.
To determine if it's a reduction or enlargement, we look at the scale factor. If the scale factor is less than 1, it's a reduction. If the scale factor is greater than 1, it's an enlargement.
In this case, since the scale factor is 1/2 (which is less than 1), the dilation is a reduction.