QuestionFind the number that completes the translation rule $T(x, y)=(x-5, y+[?])$ given points $\mathrm{P}(7,5)$ and $\mathrm{P}^{\prime}(2,8)$ .

Studdy Solution

STEP 1

Assumptions1. The original point is(7,5) . The translated point is'(,8)
3. The translation rule is(x, y) = (x-5, y+[?])
4. The x-coordinate of the translated point is obtained by subtracting5 from the x-coordinate of the original point5. The y-coordinate of the translated point is obtained by adding a certain number to the y-coordinate of the original point

STEP 2

First, we need to find the x-coordinate of the translated point using the translation rule. We do this by subtracting5 from the x-coordinate of the original point.
$_x = x -5$

STEP 3

Now, plug in the given values for the x-coordinate of the original point to calculate the x-coordinate of the translated point.
$_x =7 -5$

STEP 4

Calculate the x-coordinate of the translated point.
$_x =7 - =2$

STEP 5

Now that we have the x-coordinate of the translated point, we can see that it matches with the x-coordinate of the given translated point'(2,8). This confirms that the translation rule for the x-coordinate is correct.

STEP 6

Next, we need to find the y-coordinate of the translated point using the translation rule. We do this by adding a certain number to the y-coordinate of the original point.
$_y = y + [?]$

STEP 7

Since we know the y-coordinate of the original point (5) and the y-coordinate of the translated point (), we can set up an equation to solve for the unknown number.
$=5 + [?]$

STEP 8

Rearrange the equation to solve for the unknown number.
$[?] =8 -5$

STEP 9

Calculate the unknown number.
$[?] =8 -5 =3$ The number that belongs in the green box is3.

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QuestionFind the number that completes the translation rule $T(x, y)=(x-5, y+[?])$ given points $\mathrm{P}(7,5)$ and $\mathrm{P}^{\prime}(2,8)$ .

Studdy Solution

STEP 1

STEP 2

First, we need to find the x-coordinate of the translated point using the translation rule. We do this by subtracting5 from the x-coordinate of the original point.
$_x = x -5$

STEP 3

Now, plug in the given values for the x-coordinate of the original point to calculate the x-coordinate of the translated point.
$_x =7 -5$

STEP 4

Calculate the x-coordinate of the translated point.
$_x =7 - =2$

STEP 5

Now that we have the x-coordinate of the translated point, we can see that it matches with the x-coordinate of the given translated point'(2,8). This confirms that the translation rule for the x-coordinate is correct.

STEP 6

Next, we need to find the y-coordinate of the translated point using the translation rule. We do this by adding a certain number to the y-coordinate of the original point.
$_y = y + [?]$

STEP 7

Since we know the y-coordinate of the original point (5) and the y-coordinate of the translated point (), we can set up an equation to solve for the unknown number.
$=5 + [?]$

STEP 8

Rearrange the equation to solve for the unknown number.
$[?] =8 -5$

STEP 9

Calculate the unknown number.
$[?] =8 -5 =3$ The number that belongs in the green box is3.

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QuestionFind the number that completes the translation rule T(x,y)=(x−5,y+[?])T(x, y)=(x-5, y+[?])T(x,y)=(x−5,y+[?]) given points P(7,5)\mathrm{P}(7,5)P(7,5) and P′(2,8)\mathrm{P}^{\prime}(2,8)P′(2,8).

Studdy Solution

STEP 1

STEP 2

First, we need to find the x-coordinate of the translated point using the translation rule. We do this by subtracting5 from the x-coordinate of the original point.x=x−5_x = x -5x​=x−5

STEP 3

Now, plug in the given values for the x-coordinate of the original point to calculate the x-coordinate of the translated point.x=7−5_x =7 -5x​=7−5

STEP 4

Calculate the x-coordinate of the translated point.x=7−=2_x =7 - =2x​=7−=2

STEP 5

Now that we have the x-coordinate of the translated point, we can see that it matches with the x-coordinate of the given translated point'(2,8). This confirms that the translation rule for the x-coordinate is correct.

STEP 6

Next, we need to find the y-coordinate of the translated point using the translation rule. We do this by adding a certain number to the y-coordinate of the original point.y=y+[?]_y = y + [?]y​=y+[?]

STEP 7

Since we know the y-coordinate of the original point (5) and the y-coordinate of the translated point (), we can set up an equation to solve for the unknown number.=5+[?] =5 + [?]=5+[?]

STEP 8

Rearrange the equation to solve for the unknown number.[?]=8−5[?] =8 -5[?]=8−5

STEP 9

Calculate the unknown number.[?]=8−5=3[?] =8 -5 =3[?]=8−5=3The number that belongs in the green box is3.

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QuestionFind the number that completes the translation rule $T(x, y)=(x-5, y+[?])$ given points $\mathrm{P}(7,5)$ and $\mathrm{P}^{\prime}(2,8)$ .

First, we need to find the x-coordinate of the translated point using the translation rule. We do this by subtracting5 from the x-coordinate of the original point.
$_x = x -5$

Now, plug in the given values for the x-coordinate of the original point to calculate the x-coordinate of the translated point.
$_x =7 -5$

Calculate the x-coordinate of the translated point.
$_x =7 - =2$

Next, we need to find the y-coordinate of the translated point using the translation rule. We do this by adding a certain number to the y-coordinate of the original point.
$_y = y + [?]$

Since we know the y-coordinate of the original point (5) and the y-coordinate of the translated point (), we can set up an equation to solve for the unknown number.
$=5 + [?]$

Rearrange the equation to solve for the unknown number.
$[?] =8 -5$

Calculate the unknown number.
$[?] =8 -5 =3$ The number that belongs in the green box is3.