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Worksheet: Translation in the First Quadrant

In this worksheet, we will practice applying translation of a point or a polygon and deducing the magnitude and the direction of translation.

Q1:

Hannah wants to change the location of her rectangular desk. If she moves it only by a translation, will it fit exactly into one of the other corners of the room?

  • A yes
  • B no

Q2:

A triangular sign with vertices shown in the given table was moved. If the new coordinates for the first two vertices are ( 7 , 2 ) and ( 3 , 2 ) , determine the new coordinates for the third vertex.

Vertex 1 2 3
Coordinates ( 8 , 3 ) ( 4 , 3 ) ( 3 , 1 5 )
  • A ( 4 , 1 6 )
  • B ( 3 , 1 5 )
  • C ( 7 , 1 5 )
  • D ( 2 , 1 4 )
  • E ( βˆ’ 1 , 1 5 )

Q3:

A triangular sign with vertices shown in the given table was moved. If the new coordinates for the first two vertices are ( 9 , 5 ) and ( 5 , 1 2 ) , determine the new coordinates for the third vertex.

Vertex 1 2 3
Coordinates ( 7 , 3 ) ( 3 , 1 0 ) ( 1 4 , 8 )
  • A ( 1 2 , 6 )
  • B ( 1 4 , 8 )
  • C ( 1 8 , 1 )
  • D ( 1 6 , 1 0 )
  • E ( 1 0 , 1 5 )

Q4:

A triangular sign with vertices shown in the given table was moved. If the new coordinates for the first two vertices are ( 3 , 4 ) and ( 5 , 4 ) , determine the new coordinates for the third vertex.

Vertex 1 2 3
Coordinates ( 1 , 7 ) ( 3 , 7 ) ( 5 , 1 5 )
  • A ( 3 , 1 8 )
  • B ( 5 , 1 5 )
  • C ( 3 , 1 5 )
  • D ( 7 , 1 2 )
  • E ( 7 , 1 5 )

Q5:

A triangular sign with vertices shown in the given table was moved. If the new coordinates for the first two vertices are ( 2 , 6 ) and ( 6 , 1 0 ) , determine the new coordinates for the third vertex.

Vertex 1 2 3
Coordinates ( 7 , 7 ) ( 1 1 , 1 1 ) ( 1 5 , 8 )
  • A ( 2 0 , 9 )
  • B ( 1 5 , 8 )
  • C ( 1 1 , 4 )
  • D ( 1 0 , 7 )
  • E ( 1 9 , 1 2 )

Q6:

A triangular sign with vertices shown in the given table was moved. If the new coordinates for the first two vertices are ( 1 4 , 1 2 ) and ( 1 3 , 5 ) , determine the new coordinates for the third vertex.

Vertex 1 2 3
Coordinates ( 1 3 , 1 5 ) ( 1 2 , 8 ) ( 1 3 , 1 3 )
  • A ( 1 2 , 1 6 )
  • B ( 1 3 , 1 3 )
  • C ( 1 4 , 2 0 )
  • D ( 1 4 , 1 0 )
  • E ( 1 2 , 6 )

Q7:

Two points 𝐴 and 𝐡 have coordinates (7, 2) and (7, 5) respectively. 𝐴 𝐡 is translated three right and two down to 𝐴 𝐡   .

Determine the coordinates of 𝐴 β€² and 𝐡 β€² .

  • A 𝐴 β€² = ( 4 , 0 ) , 𝐡 β€² = ( 4 , 3 )
  • B 𝐴 β€² = ( 0 , 1 0 ) , 𝐡 β€² = ( 3 , 1 0 )
  • C 𝐴 β€² = ( 1 0 , 4 ) , 𝐡 β€² = ( 1 0 , 7 )
  • D 𝐴 β€² = ( 1 0 , 0 ) , 𝐡 β€² = ( 1 0 , 3 )
  • E 𝐴 β€² = ( 4 , 4 ) , 𝐡 β€² = ( 4 , 7 )

Is the length of 𝐴 𝐡 greater than, less than, or equal to the length of 𝐴 β€² 𝐡 β€² ?

  • Aequal to
  • Bless than
  • Cgreater than

Q8:

A triangular table was positioned with its corners at the coordinates ( 2 , 4 ) , ( 0 , 6 ) , and ( 1 , 1 ) . It was later moved to new coordinates ( 0 , 8 ) , ( βˆ’ 2 , 1 0 ) , and ( βˆ’ 1 , 5 ) . Describe the translation.

  • A It was moved 2 units to the right and 12 units up.
  • B It was moved 2 units to the right and 4 units down.
  • C It was moved 2 units to the left and 12 units down.
  • D It was moved 2 units to the left and 4 units up.

Q9:

A triangular table was positioned with its corners at the coordinates ( 2 , 3 ) , ( 5 , 1 ) , and ( 7 , 5 ) . It was later moved to new coordinates ( 6 , 5 ) , ( 9 , 3 ) , and ( 1 1 , 7 ) . Describe the translation.

  • A It was moved 8 units to the right and 8 units up.
  • B It was moved 4 units to the left and 2 units down.
  • C It was moved 8 units to the left and 8 units down.
  • D It was moved 4 units to the right and 2 units up.

Q10:

A triangular table was positioned with its corners at the coordinates ( 7 , 4 ) , ( 4 , 6 ) , and ( 1 , 3 ) . It was later moved to new coordinates ( 1 1 , 6 ) , ( 8 , 8 ) , and ( 5 , 5 ) . Describe the translation.

  • A It was moved 18 units to the right and 10 units up.
  • B It was moved 4 units to the left and 2 units down.
  • C It was moved 18 units to the left and 10 units down.
  • D It was moved 4 units to the right and 2 units up.

Q11:

A triangular table was positioned with its corners at the coordinates ( 4 , 5 ) , ( 7 , 1 ) , and ( 5 , 7 ) . It was later moved to new coordinates ( 2 , 9 ) , ( 5 , 5 ) , and ( 3 , 1 1 ) . Describe the translation.

  • A It was moved 6 units to the right and 14 units up.
  • B It was moved 2 units to the right and 4 units down.
  • C It was moved 6 units to the left and 14 units down.
  • D It was moved 2 units to the left and 4 units up.

Q12:

A triangular table was positioned with its corners at the coordinates ( 4 , 6 ) , ( 0 , 5 ) , and ( 3 , 4 ) . It was later moved to new coordinates ( 5 , 1 0 ) , ( 1 , 9 ) , and ( 4 , 8 ) . Describe the translation.

  • A It was moved 9 units to the right and 16 units up.
  • B It was moved 1 unit to the left and 4 units down.
  • C It was moved 9 units to the left and 16 units down.
  • D It was moved 1 unit to the right and 4 units up.

Q13:

A line segment with a length of 5 is translated three left and two down. What is the length of its image?

Q14:

Two intersecting lines are translated three left and eleven right. Is it possible for the images of the two lines to be parallel?

  • Ano
  • Byes

Q15:

Triangle 𝐴 𝐡 𝐢 has been translated to obtain triangle 𝐴 𝐡 𝐢 β€² β€² β€² as seen in the given figure. Work out the perimeter of the triangle 𝐴 𝐡 𝐢 . Give your solution accurate to two decimal places.

Q16:

In the given figure, 𝐴 𝐡 𝐢 𝐷 is a square, and all the interior squares are congruent. Find the image of 𝐴 𝐸 after a translation of 3 cm in the direction of  𝐺 𝑋 .

  • A 𝐹 𝐡
  • B 𝐸 𝐹
  • C 𝑀 𝑁
  • D 𝐷 π‘Œ

Q17:

In the given figure, 𝐴 𝐡 𝐢 𝐷 is a square, and all the interior squares are congruent. Find the image of 𝐺 𝐿 after a translation of 4.3 cm in the direction of  𝐾 𝐹 .

  • A 𝑀 𝑁
  • B 𝑁 𝐺
  • C 𝑋 𝐢
  • D 𝐹 𝐡

Q18:

Describe the single transformation that would map triangle 𝐴 𝐡 𝐢 onto triangle 𝐴 β€² 𝐡 β€² 𝐢 β€² in the given figure.

  • A a translation seven left and two up
  • B a translation two right and seven down
  • C a translation seven right and two up
  • D a translation seven right and two down
  • Ea translation seven left and two down

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