Solved on Nov 04, 2023

Find the point obtained by dilating (0,6) by a scale factor of 1/3 around the origin.

STEP 1

Assumptions1. The original point is $(0,6)$ . The dilation is centered at the origin (0,0)
3. The scale factor of the dilation is $\frac{1}{3}$

STEP 2

In a dilation, each coordinate of the original point is multiplied by the scale factor to get the coordinates of the image. $Image(x,y) = (Original\, x \times Scale\, factor, Original\, y \times Scale\, factor)$

STEP 3

Now, plug in the given values for the original point and the scale factor to calculate the image.
$Image(x,y) = (0 \times \frac{1}{3},6 \times \frac{1}{3})$

STEP 4

Calculate the x-coordinate of the image.
$Image\, x =0 \times \frac{1}{3} =0$

STEP 5

Calculate the y-coordinate of the image.
$Image\, y = \times \frac{1}{3} =2$

STEP 6

Now that we have the x and y coordinates of the image, we can write them as a coordinate pair.
$Image = (Image\, x, Image\, y)$

STEP 7

Plug in the values for the image x and y to get the image point.
$Image = (0,2)$ The image of $(0,6)$ after a dilation by a scale factor of $\frac{1}{3}$ centered at the origin is $(0,2)$ .

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Find the point obtained by dilating (0,6) by a scale factor of 1/3 around the origin.

STEP 1

Assumptions1. The original point is $(0,6)$ . The dilation is centered at the origin (0,0)
3. The scale factor of the dilation is $\frac{1}{3}$

STEP 2

In a dilation, each coordinate of the original point is multiplied by the scale factor to get the coordinates of the image. $Image(x,y) = (Original\, x \times Scale\, factor, Original\, y \times Scale\, factor)$

STEP 3

Now, plug in the given values for the original point and the scale factor to calculate the image.
$Image(x,y) = (0 \times \frac{1}{3},6 \times \frac{1}{3})$

STEP 4

Calculate the x-coordinate of the image.
$Image\, x =0 \times \frac{1}{3} =0$

STEP 5

Calculate the y-coordinate of the image.
$Image\, y = \times \frac{1}{3} =2$

STEP 6

Now that we have the x and y coordinates of the image, we can write them as a coordinate pair.
$Image = (Image\, x, Image\, y)$

STEP 7

Plug in the values for the image x and y to get the image point.
$Image = (0,2)$ The image of $(0,6)$ after a dilation by a scale factor of $\frac{1}{3}$ centered at the origin is $(0,2)$ .

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Find the point obtained by dilating (0,6) by a scale factor of 1/3 around the origin.

STEP 1

Assumptions1. The original point is (0,6)(0,6)(0,6). The dilation is centered at the origin (0,0)3. The scale factor of the dilation is 13\frac{1}{3}31​

STEP 2

STEP 3

Now, plug in the given values for the original point and the scale factor to calculate the image.Image(x,y)=(0×13,6×13)Image(x,y) = (0 \times \frac{1}{3},6 \times \frac{1}{3})Image(x,y)=(0×31​,6×31​)

STEP 4

Calculate the x-coordinate of the image.Image x=0×13=0Image\, x =0 \times \frac{1}{3} =0Imagex=0×31​=0

STEP 5

Calculate the y-coordinate of the image.Image y=×13=2Image\, y = \times \frac{1}{3} =2Imagey=×31​=2

STEP 6

Now that we have the x and y coordinates of the image, we can write them as a coordinate pair.Image=(Image x,Image y)Image = (Image\, x, Image\, y)Image=(Imagex,Imagey)

STEP 7

Plug in the values for the image x and y to get the image point.Image=(0,2)Image = (0,2)Image=(0,2)The image of (0,6)(0,6)(0,6) after a dilation by a scale factor of 13\frac{1}{3}31​ centered at the origin is (0,2)(0,2)(0,2).

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Assumptions1. The original point is $(0,6)$ . The dilation is centered at the origin (0,0)
3. The scale factor of the dilation is $\frac{1}{3}$

Now, plug in the given values for the original point and the scale factor to calculate the image.
$Image(x,y) = (0 \times \frac{1}{3},6 \times \frac{1}{3})$

Calculate the x-coordinate of the image.
$Image\, x =0 \times \frac{1}{3} =0$

Calculate the y-coordinate of the image.
$Image\, y = \times \frac{1}{3} =2$

Now that we have the x and y coordinates of the image, we can write them as a coordinate pair.
$Image = (Image\, x, Image\, y)$

Plug in the values for the image x and y to get the image point.
$Image = (0,2)$ The image of $(0,6)$ after a dilation by a scale factor of $\frac{1}{3}$ centered at the origin is $(0,2)$ .