QuestionFind the translation from $Q(3,6)$ to $Q^{\prime}(9,3)$ as $\langle x, y\rangle$ . Show your work.

Studdy Solution

STEP 1

Assumptions1. The coordinates of point Q are (3,6) . The coordinates of point Q' are (9,3)
3. The translation maps point Q to point Q'

STEP 2

A translation in the plane can be described by a pair of numbers, $\langle x, y\rangle$ , where $x$ is the horizontal shift and $y$ is the vertical shift.

STEP 3

To find the horizontal shift, subtract the x-coordinate of point Q from the x-coordinate of point Q'.
$x = x_{Q'} - x_{Q}$

STEP 4

Plug in the given x-coordinates to calculate the horizontal shift.
$x =9 -3$

STEP 5

Calculate the horizontal shift.
$x =9 -3 =$

STEP 6

To find the vertical shift, subtract the y-coordinate of point Q from the y-coordinate of point Q'.
$y = y_{Q'} - y_{Q}$

STEP 7

Plug in the given y-coordinates to calculate the vertical shift.
$y =3 -6$

STEP 8

Calculate the vertical shift.
$y =3 -6 = -3$

STEP 9

Now that we have the horizontal and vertical shifts, we can write the translation in the form $\langle x, y\rangle$ .
$Translation = \langle x, y\rangle$

STEP 10

Plug in the values for the horizontal and vertical shifts to write the translation.
$Translation = \langle6, -3\rangle$ The translation that maps Q to Q' is $\langle6, -3\rangle$ .

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QuestionFind the translation from $Q(3,6)$ to $Q^{\prime}(9,3)$ as $\langle x, y\rangle$ . Show your work.

Studdy Solution

STEP 1

Assumptions1. The coordinates of point Q are (3,6) . The coordinates of point Q' are (9,3)
3. The translation maps point Q to point Q'

STEP 2

A translation in the plane can be described by a pair of numbers, $\langle x, y\rangle$ , where $x$ is the horizontal shift and $y$ is the vertical shift.

STEP 3

To find the horizontal shift, subtract the x-coordinate of point Q from the x-coordinate of point Q'.
$x = x_{Q'} - x_{Q}$

STEP 4

Plug in the given x-coordinates to calculate the horizontal shift.
$x =9 -3$

STEP 5

Calculate the horizontal shift.
$x =9 -3 =$

STEP 6

To find the vertical shift, subtract the y-coordinate of point Q from the y-coordinate of point Q'.
$y = y_{Q'} - y_{Q}$

STEP 7

Plug in the given y-coordinates to calculate the vertical shift.
$y =3 -6$

STEP 8

Calculate the vertical shift.
$y =3 -6 = -3$

STEP 9

Now that we have the horizontal and vertical shifts, we can write the translation in the form $\langle x, y\rangle$ .
$Translation = \langle x, y\rangle$

STEP 10

Plug in the values for the horizontal and vertical shifts to write the translation.
$Translation = \langle6, -3\rangle$ The translation that maps Q to Q' is $\langle6, -3\rangle$ .

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QuestionFind the translation from Q(3,6)Q(3,6)Q(3,6) to Q′(9,3)Q^{\prime}(9,3)Q′(9,3) as ⟨x,y⟩\langle x, y\rangle⟨x,y⟩. Show your work.

Studdy Solution

STEP 1

Assumptions1. The coordinates of point Q are (3,6) . The coordinates of point Q' are (9,3)3. The translation maps point Q to point Q'

STEP 2

A translation in the plane can be described by a pair of numbers, ⟨x,y⟩\langle x, y\rangle⟨x,y⟩, where xxx is the horizontal shift and yyy is the vertical shift.

STEP 3

To find the horizontal shift, subtract the x-coordinate of point Q from the x-coordinate of point Q'.x=xQ′−xQx = x_{Q'} - x_{Q}x=xQ′​−xQ​

STEP 4

Plug in the given x-coordinates to calculate the horizontal shift.x=9−3x =9 -3x=9−3

STEP 5

Calculate the horizontal shift.x=9−3=x =9 -3 =x=9−3=

STEP 6

To find the vertical shift, subtract the y-coordinate of point Q from the y-coordinate of point Q'.y=yQ′−yQy = y_{Q'} - y_{Q}y=yQ′​−yQ​

STEP 7

Plug in the given y-coordinates to calculate the vertical shift.y=3−6y =3 -6y=3−6

STEP 8

Calculate the vertical shift.y=3−6=−3y =3 -6 = -3y=3−6=−3

STEP 9

Now that we have the horizontal and vertical shifts, we can write the translation in the form ⟨x,y⟩\langle x, y\rangle⟨x,y⟩.Translation=⟨x,y⟩Translation = \langle x, y\rangleTranslation=⟨x,y⟩

STEP 10

Plug in the values for the horizontal and vertical shifts to write the translation.Translation=⟨6,−3⟩Translation = \langle6, -3\rangleTranslation=⟨6,−3⟩The translation that maps Q to Q' is ⟨6,−3⟩\langle6, -3\rangle⟨6,−3⟩.

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QuestionFind the translation from $Q(3,6)$ to $Q^{\prime}(9,3)$ as $\langle x, y\rangle$ . Show your work.

Assumptions1. The coordinates of point Q are (3,6) . The coordinates of point Q' are (9,3)
3. The translation maps point Q to point Q'

A translation in the plane can be described by a pair of numbers, $\langle x, y\rangle$ , where $x$ is the horizontal shift and $y$ is the vertical shift.

To find the horizontal shift, subtract the x-coordinate of point Q from the x-coordinate of point Q'.
$x = x_{Q'} - x_{Q}$

Plug in the given x-coordinates to calculate the horizontal shift.
$x =9 -3$

Calculate the horizontal shift.
$x =9 -3 =$

To find the vertical shift, subtract the y-coordinate of point Q from the y-coordinate of point Q'.
$y = y_{Q'} - y_{Q}$

Plug in the given y-coordinates to calculate the vertical shift.
$y =3 -6$

Calculate the vertical shift.
$y =3 -6 = -3$

Now that we have the horizontal and vertical shifts, we can write the translation in the form $\langle x, y\rangle$ .
$Translation = \langle x, y\rangle$

Plug in the values for the horizontal and vertical shifts to write the translation.
$Translation = \langle6, -3\rangle$ The translation that maps Q to Q' is $\langle6, -3\rangle$ .