Question

Which graph shows a dilation of a rectangle with a scale Factor of 1/3?

Answer 1

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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