Note: As you have not attached any graph to chose the answer. So, that is I am taking a quadrilateral ABCD as sample figure to clear your concept as it would still clear your concept regarding dilation by a factor 1/3 about the origin.
Answer:
When the quadrilateral ABCD with vertices A(-6, -3), B(-6, 3), C(6, 3) and D(6, -3) respectively is dilated by a factor 1/3 about the origin, the reduced image A'B'C'D' with vertices A(-2, -1), B(-2, 1), C(2, 1) and D(2, -1) is obtained as shown in figure a.
Step-by-step explanation:
Considering the quadrilateral ABCD, as shown in figure a, with the following vertices
As we know that a dilation is a transformation that generates an image that contains the same shape as the original object, but has a different size.
- A dilation that creates a bigger image than the original object is called an enlargement.
- A dilation that creates a smaller image than the original object is called an reduction.
If
scale factor [tex]> 1[/tex], the image will be a stretch or enlargement.
and if
[tex]0<[/tex] scale factor [tex]<1[/tex], the image will be be a shrink or reduction.
The rule of dilation by a factor 1/3 about the origin:
Dilation with scale factor 1/3, just multiply the coordinates of vertices by 1/3.
[tex](x, y)[/tex] → [tex](\frac{1}{3}x, \frac{1}{3}y)[/tex]
So,
When the quadrilateral ABCD with vertices A(-6, -3), B(-6, 3), C(6, 3) and D(6, -3) respectively is dilated by a factor 1/3 about the origin, the reduced image A'B'C'D' with vertices A(-2, -1), B(-2, 1), C(2, 1) and D(2, -1) is obtained as shown in figure a.
Therefore,
[tex](x, y)[/tex] → [tex](\frac{1}{3}x, \frac{1}{3}y)[/tex]
[tex]A(-6, -3)[/tex] → [tex]A'(-2, -1)[/tex]
[tex]B(-6, 3)[/tex] → [tex]B'(-2, 1)[/tex]
[tex]C(6, 3)[/tex] → [tex]C'(2, 1)[/tex]
[tex]D(6, -3)[/tex] → [tex]D'(2, -1)[/tex]
Keywords: dilation, scale factor, image, quadrilateral
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