J K → \overrightarrow{JK} J K <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

K J → \overrightarrow{KJ} K J <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

Write a translation rule for the translation from Δ R S T t o Δ R ′ S ′ T ′ \Delta RST\ to\ \Delta R'S'T' Δ R S T t o Δ R ′ S ′ T ′ Look carefully at the increments on the graph!

( x , y ) → ( x + 6 , y + 4 ) \left(x,y\right)\rightarrow\left(x+6,\ y+4\right) ( x , y ) → ( x + 6 , y + 4 )

( x , y ) → ( x + 3 , y + 2 ) \left(x,\ y\right)\rightarrow\left(x+3,\ y+2\right) ( x , y ) → ( x + 3 , y + 2 )

( x , y ) → ( x − 3 , y − 2 ) \left(x,\ y\right)\rightarrow\left(x-3,\ y-2\right) ( x , y ) → ( x − 3 , y − 2 )

( x , y ) → ( x − 6 , y − 4 ) \left(x,\ y\right)\rightarrow\left(x-6,\ y-4\right) ( x , y ) → ( x − 6 , y − 4 )

Use the translation ( x , y ) → ( x + 1 , y − 3 ) \left(x,\ y\right)\rightarrow\left(x+1,\ y-3\right) ( x , y ) → ( x + 1 , y − 3 ) to find the image of the point Q(5, 9).

Q ′ ( 6 , 6 ) Q'\ \left(6,\ 6\right) Q ′ ( 6 , 6 )

Q ′ ( 4 , 10 ) Q'\ \left(4,\ 10\right) Q ′ ( 4 , 1 0 )

Q ′ ( 6 , 10 ) Q'\ \left(6,\ 10\right) Q ′ ( 6 , 1 0 )

Q ′ ( 4 , 6 ) Q'\ \left(4,\ 6\right) Q ′ ( 4 , 6 )

Find the image of P ( 3 , 4 ) P\left(3,\ 4\right) P ( 3 , 4 ) after the composition of translations ( x , y ) → ( x + 1 , y − 2 ) \left(x,\ y\right)\rightarrow\left(x+1,\ y-2\right) ( x , y ) → ( x + 1 , y − 2 ) and ( x , y ) → ( x − 5 , y + 1 ) \left(x,\ y\right)\rightarrow\left(x-5,\ y+1\right) ( x , y ) → ( x − 5 , y + 1 )

( − 1 , 3 ) \left(-1,\ 3\right) ( − 1 , 3 )

( − 2 , 5 ) \left(-2,\ 5\right) ( − 2 , 5 )

( 4 , 2 ) \left(4,\ 2\right) ( 4 , 2 )

( 2 , 6 ) \left(2,\ 6\right) ( 2 , 6 )

Find the image of D ( 0 , − 2 ) D\left(0,\ -2\right) D ( 0 , − 2 ) after the composition of translations ( x , y ) → ( x + 10 , y − 8 ) \left(x,\ y\right)\rightarrow\left(x+10,\ y-8\right) ( x , y ) → ( x + 1 0 , y − 8 ) and ( x , y ) → ( x − 7 , y + 15 ) \left(x,\ y\right)\rightarrow\left(x-7,\ y+15\right) ( x , y ) → ( x − 7 , y + 1 5 )

( 3 , 5 ) \left(3,\ 5\right) ( 3 , 5 )

( 10 , − 10 ) \left(10,\ -10\right) ( 1 0 , − 1 0 )

( − 7 , 13 ) \left(-7,\ 13\right) ( − 7 , 1 3 )

( − 4 , 8 ) \left(-4,\ 8\right) ( − 4 , 8 )

Find the component form of the vector that translates A ( 3 , − 2 ) t o A ′ ( − 1 , 4 ) A\left(3,-2\right)\ to\ A'\left(-1,4\right) A ( 3 , − 2 ) t o A ′ ( − 1 , 4 )

< − 4 , 6 > <-4,\ 6> < − 4 , 6 >

< − 4 , 2 > <-4,\ 2> < − 4 , 2 >

#4.1 Translations

Authored by Stephanie DiBari

Mathematics

10th Grade

CCSS covered

Used 57+ times

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10 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Name the vector

$\overrightarrow{JK}$

$\overrightarrow{KJ}$

$\overline{JK}$

$\overline{KJ}$

Tags

CCSS.HSG.CO.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Write the vector's component form.

$<2,\ -3>$

$<-3,\ 2>$

$<-2,\ 3>$

$<3,\ -2>$

Tags

CCSS.HSN.VM.A.1

CCSS.HSN.VM.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The vertices of
$\Delta ABC$ are A(2, 1), B(-6, 4), and C(-3, -2). Translate the triangle using vector $<-1,\ 3>$ . What are the coordinates of the image?

A(1,4), B(-7,7), C(-2, 5)

A(3, 2), B(-5, 1), C(-2, 1)

A(1,4), B(-7, 7), C(-4, 1)

A(3, 2), B(-5, 1), C(-4, 5)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Write a translation rule for the translation from $\Delta RST\ to\ \Delta R'S'T'$
Look carefully at the increments on the graph!

$\left(x,\ y\right)\rightarrow\left(x+3,\ y+2\right)$

$\left(x,\ y\right)\rightarrow\left(x-3,\ y-2\right)$

$\left(x,\ y\right)\rightarrow\left(x-6,\ y-4\right)$

$\left(x,y\right)\rightarrow\left(x+6,\ y+4\right)$

Tags

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What are the coordinates of the vertices of the image after the translation is applied? $\left(x,\ y\right)\rightarrow\left(x+2,\ y-1\right)$

A (-1, 3) and B(4, -4)

A (-5, 5) and B (4, -2)

A (-6, -4) and B (4, 4)

A (4, -4) and B (-2, 7)

Tags

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Use the translation $\left(x,\ y\right)\rightarrow\left(x+1,\ y-3\right)$ to find the image of the point Q(5, 9).

$Q'\ \left(6,\ 6\right)$

$Q'\ \left(4,\ 10\right)$

$Q'\ \left(6,\ 10\right)$

$Q'\ \left(4,\ 6\right)$

Tags

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the image of $P\left(3,\ 4\right)$ after the composition of translations $\left(x,\ y\right)\rightarrow\left(x+1,\ y-2\right)$ and $\left(x,\ y\right)\rightarrow\left(x-5,\ y+1\right)$

$\left(-2,\ 5\right)$

$\left(4,\ 2\right)$

$\left(-1,\ 3\right)$

$\left(2,\ 6\right)$

Tags

CCSS.8.G.A.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the image of $D\left(0,\ -2\right)$ after the composition of translations $\left(x,\ y\right)\rightarrow\left(x+10,\ y-8\right)$ and $\left(x,\ y\right)\rightarrow\left(x-7,\ y+15\right)$

$\left(3,\ 5\right)$

$\left(10,\ -10\right)$

$\left(-7,\ 13\right)$

$\left(-4,\ 8\right)$

Tags

CCSS.8.G.A.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Write the vector's component form. (Assume the units on the graph are 1)

$<3,\ 6>$

$<-3,\ -6>$

$<6,\ 3>$

$<-6,\ -3>$

Tags

CCSS.HSG.CO.A.2

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the component form of the vector that translates

$A\left(3,-2\right)\ to\ A'\left(-1,4\right)$

$<-4,\ 2>$

$<2,\ 2>$

$<-4,\ 6>$

$<2,\ 6>$

Tags

CCSS.HSG.CO.A.2

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#4.1 Translations

Name the vector

Write the vector's component form.

The vertices of ΔABC\Delta ABCΔABC are A(2, 1), B(-6, 4), and C(-3, -2). Translate the triangle using vector <−1, 3><-1,\ 3><−1, 3> . What are the coordinates of the image?

Write a translation rule for the translation from ΔRST to ΔR′S′T′\Delta RST\ to\ \Delta R'S'T'ΔRST to ΔR′S′T′ Look carefully at the increments on the graph!

What are the coordinates of the vertices of the image after the translation is applied? (x, y)→(x+2, y−1)\left(x,\ y\right)\rightarrow\left(x+2,\ y-1\right)(x, y)→(x+2, y−1)

Use the translation (x, y)→(x+1, y−3)\left(x,\ y\right)\rightarrow\left(x+1,\ y-3\right)(x, y)→(x+1, y−3) to find the image of the point Q(5, 9).

Find the image of P(3, 4)P\left(3,\ 4\right)P(3, 4) after the composition of translations (x, y)→(x+1, y−2)\left(x,\ y\right)\rightarrow\left(x+1,\ y-2\right)(x, y)→(x+1, y−2) and (x, y)→(x−5, y+1)\left(x,\ y\right)\rightarrow\left(x-5,\ y+1\right)(x, y)→(x−5, y+1)

Find the image of D(0, −2)D\left(0,\ -2\right)D(0, −2) after the composition of translations (x, y)→(x+10, y−8)\left(x,\ y\right)\rightarrow\left(x+10,\ y-8\right)(x, y)→(x+10, y−8) and (x, y)→(x−7, y+15)\left(x,\ y\right)\rightarrow\left(x-7,\ y+15\right)(x, y)→(x−7, y+15)

Write the vector's component form. (Assume the units on the graph are 1)

Find the component form of the vector that translates A(3,−2) to A′(−1,4)A\left(3,-2\right)\ to\ A'\left(-1,4\right)A(3,−2) to A′(−1,4)

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Discover more resources for Mathematics

The vertices of
$\Delta ABC$ are A(2, 1), B(-6, 4), and C(-3, -2). Translate the triangle using vector $<-1,\ 3>$ . What are the coordinates of the image?

Write a translation rule for the translation from $\Delta RST\ to\ \Delta R'S'T'$
Look carefully at the increments on the graph!

What are the coordinates of the vertices of the image after the translation is applied? $\left(x,\ y\right)\rightarrow\left(x+2,\ y-1\right)$

Use the translation $\left(x,\ y\right)\rightarrow\left(x+1,\ y-3\right)$ to find the image of the point Q(5, 9).

Find the image of $P\left(3,\ 4\right)$ after the composition of translations $\left(x,\ y\right)\rightarrow\left(x+1,\ y-2\right)$ and $\left(x,\ y\right)\rightarrow\left(x-5,\ y+1\right)$

Find the image of $D\left(0,\ -2\right)$ after the composition of translations $\left(x,\ y\right)\rightarrow\left(x+10,\ y-8\right)$ and $\left(x,\ y\right)\rightarrow\left(x-7,\ y+15\right)$

Find the component form of the vector that translates

$A\left(3,-2\right)\ to\ A'\left(-1,4\right)$