Question

Which graph shows the result of dilating this figure by a factor 1/3 about the origin

Answer 1

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

• A(-6, -3)

• B(-6, 3)

• C(6, 3)

• D(6, -3)

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 $> 1$, the image will be a stretch or enlargement.

and if

$0$ scale factor , 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.

$(x, y)$ → $(\frac{1}{3}x, \frac{1}{3}y)$

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,

   $(x, y)$        →      $(\frac{1}{3}x, \frac{1}{3}y)$

$A(-6, -3)$    →     $A'(-2, -1)$

$B(-6, 3)$       →     $B'(-2, 1)$

$C(6, 3)$          →     $C'(2, 1)$

$D(6, -3)$       →    $D'(2, -1)$

Keywords: dilation, scale factor, image, quadrilateral

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Answer 2

Answer:

hope this helped

Step-by-step explanation: