Solved on Feb 28, 2024

Find the coordinates of point $Z'$ given that point $Z$ has coordinates $(-3,5)$ and is translated left 2 units and down 2 units.

STEP 1

Assumptions
1. The original coordinates of point $Z$ are $(-3,5)$ .
2. A translation left means a decrease in the x-coordinate.
3. A translation down means a decrease in the y-coordinate.
4. The translation is 2 units left and 2 units down.

STEP 2

To translate a point left, we subtract from its x-coordinate.
$x_{Z'} = x_Z - \text{translation left}$

STEP 3

Now, plug in the given values for the x-coordinate of point $Z$ and the translation left.
$x_{Z'} = -3 - 2$

STEP 4

Calculate the new x-coordinate for point $Z'$ .
$x_{Z'} = -3 - 2 = -5$

STEP 5

To translate a point down, we subtract from its y-coordinate.
$y_{Z'} = y_Z - \text{translation down}$

STEP 6

Now, plug in the given values for the y-coordinate of point $Z$ and the translation down.
$y_{Z'} = 5 - 2$

STEP 7

Calculate the new y-coordinate for point $Z'$ .
$y_{Z'} = 5 - 2 = 3$

STEP 8

Combine the new x-coordinate and y-coordinate to form the coordinates of point $Z'$ .
$Z' = (x_{Z'}, y_{Z'})$

STEP 9

Plug in the calculated values for $x_{Z'}$ and $y_{Z'}$ into the ordered pair.
$Z' = (-5, 3)$
The coordinates of point $Z'$ after the translation are $(-5, 3)$ .

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Find the coordinates of point $Z'$ given that point $Z$ has coordinates $(-3,5)$ and is translated left 2 units and down 2 units.

STEP 1

Assumptions
1. The original coordinates of point $Z$ are $(-3,5)$ .
2. A translation left means a decrease in the x-coordinate.
3. A translation down means a decrease in the y-coordinate.
4. The translation is 2 units left and 2 units down.

STEP 2

To translate a point left, we subtract from its x-coordinate.
$x_{Z'} = x_Z - \text{translation left}$

STEP 3

Now, plug in the given values for the x-coordinate of point $Z$ and the translation left.
$x_{Z'} = -3 - 2$

STEP 4

Calculate the new x-coordinate for point $Z'$ .
$x_{Z'} = -3 - 2 = -5$

STEP 5

To translate a point down, we subtract from its y-coordinate.
$y_{Z'} = y_Z - \text{translation down}$

STEP 6

Now, plug in the given values for the y-coordinate of point $Z$ and the translation down.
$y_{Z'} = 5 - 2$

STEP 7

Calculate the new y-coordinate for point $Z'$ .
$y_{Z'} = 5 - 2 = 3$

STEP 8

Combine the new x-coordinate and y-coordinate to form the coordinates of point $Z'$ .
$Z' = (x_{Z'}, y_{Z'})$

STEP 9

Plug in the calculated values for $x_{Z'}$ and $y_{Z'}$ into the ordered pair.
$Z' = (-5, 3)$
The coordinates of point $Z'$ after the translation are $(-5, 3)$ .

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Find the coordinates of point Z′Z'Z′ given that point ZZZ has coordinates (−3,5)(-3,5)(−3,5) and is translated left 2 units and down 2 units.

STEP 1

Assumptions1. The original coordinates of point ZZZ are (−3,5)(-3,5)(−3,5).2. A translation left means a decrease in the x-coordinate.3. A translation down means a decrease in the y-coordinate.4. The translation is 2 units left and 2 units down.

STEP 2

To translate a point left, we subtract from its x-coordinate.xZ′=xZ−translation leftx_{Z'} = x_Z - \text{translation left}xZ′​=xZ​−translation left

STEP 3

Now, plug in the given values for the x-coordinate of point ZZZ and the translation left.xZ′=−3−2x_{Z'} = -3 - 2xZ′​=−3−2

STEP 4

Calculate the new x-coordinate for point Z′Z'Z′.xZ′=−3−2=−5x_{Z'} = -3 - 2 = -5xZ′​=−3−2=−5

STEP 5

To translate a point down, we subtract from its y-coordinate.yZ′=yZ−translation downy_{Z'} = y_Z - \text{translation down}yZ′​=yZ​−translation down

STEP 6

Now, plug in the given values for the y-coordinate of point ZZZ and the translation down.yZ′=5−2y_{Z'} = 5 - 2yZ′​=5−2

STEP 7

Calculate the new y-coordinate for point Z′Z'Z′.yZ′=5−2=3y_{Z'} = 5 - 2 = 3yZ′​=5−2=3

STEP 8

Combine the new x-coordinate and y-coordinate to form the coordinates of point Z′Z'Z′.Z′=(xZ′,yZ′)Z' = (x_{Z'}, y_{Z'})Z′=(xZ′​,yZ′​)

STEP 9

Plug in the calculated values for xZ′x_{Z'}xZ′​ and yZ′y_{Z'}yZ′​ into the ordered pair.Z′=(−5,3)Z' = (-5, 3)Z′=(−5,3)The coordinates of point Z′Z'Z′ after the translation are (−5,3)(-5, 3)(−5,3).

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Find the coordinates of point $Z'$ given that point $Z$ has coordinates $(-3,5)$ and is translated left 2 units and down 2 units.

Assumptions
1. The original coordinates of point $Z$ are $(-3,5)$ .
2. A translation left means a decrease in the x-coordinate.
3. A translation down means a decrease in the y-coordinate.
4. The translation is 2 units left and 2 units down.

To translate a point left, we subtract from its x-coordinate.
$x_{Z'} = x_Z - \text{translation left}$

Now, plug in the given values for the x-coordinate of point $Z$ and the translation left.
$x_{Z'} = -3 - 2$

Calculate the new x-coordinate for point $Z'$ .
$x_{Z'} = -3 - 2 = -5$

To translate a point down, we subtract from its y-coordinate.
$y_{Z'} = y_Z - \text{translation down}$

Now, plug in the given values for the y-coordinate of point $Z$ and the translation down.
$y_{Z'} = 5 - 2$

Calculate the new y-coordinate for point $Z'$ .
$y_{Z'} = 5 - 2 = 3$

Combine the new x-coordinate and y-coordinate to form the coordinates of point $Z'$ .
$Z' = (x_{Z'}, y_{Z'})$

Plug in the calculated values for $x_{Z'}$ and $y_{Z'}$ into the ordered pair.
$Z' = (-5, 3)$
The coordinates of point $Z'$ after the translation are $(-5, 3)$ .