Answer:
The first picture corresponds the correct dilation by a scale of factor of 1/3 as the image rectangle is reduced and has the coordinates (-2, 0), (0, 2), (2, 0), and (0, -2) after a rectangle is dilated by a scale of factor of 1/3.
Step-by-step explanation:
A dilation is said to be a transformation which generates an image that is the same shape as the original object, but has a different size.
If the scale factor is greater than 1, then the image will be enlarged. In other words,
- scale factor > 1, image will be enlarged
If the scale factor is greater than 0 but less than 1, then the image will be reduced. In other words,
- 0 < scale factor > 1, the image will be reduced
Considering the quadrilateral with the vertices (-6, 0), (0, 6), (6, 0) and (0, -6).
According to dilation rule, when a figure is dilated by a scale of factor of 1/3, the the coordinates of that point are multiplied by 1/3. So,
(x, y) → (1/3x, 1/3y)
So, lets apply this on the quadrilateral with the vertices (-6, 0), (0, 6), (6, 0) and (0, -6).
For (-6, 0)
(x, y) → (1/3x, 1/3y) = (-6, 0) → (-2, 0)
For (0, 6)
(x, y) → (1/3x, 1/3y) = (0, 6) → (0, 2)
For (6, 0)
(x, y) → (1/3x, 1/3y) = (6, 0) → (2, 0)
For (0, -6)
(x, y) → (1/3x, 1/3y) = (0, -6) → (0, -2)
So, the image rectangle will have the coordinates (-2, 0), (0, 2), (2, 0), and (0, -2) after a rectangle is dilated by a scale of factor of 1/3.
Therefore, the first picture corresponds the correct dilation by a scale of factor of 1/3 as the image rectangle is reduced and has the coordinates (-2, 0), (0, 2), (2, 0), and (0, -2) after a rectangle is dilated by a scale of factor of 1/3.
So, correct picture is also attached below.
Keywords: dilation, transformation, quadrilateral
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