Lesson Worksheet: Translation Using Vectors Mathematics

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In this worksheet, we will learn describing translations using vectors and translating a shape given a vector.

Q1:

A translation of 3 units right and 2 units down can be described by the vector 3−2.

Describe the translation from point 𝐴 to point 𝐵 using a vector.

  • A35
  • B−3−5
  • C53
  • D32
  • E−5−3

The point (1,−4) is translated using the vector −52. What are the coordinates of its image?

  • A(−4,−2)
  • B(−2,−4)
  • C(6,−6)
  • D(−5,2)

Q2:

Shape A has been translated to Shape B and then to Shape C.

Write a vector to represent the translation from Shape A to Shape B.

  • A26
  • B52
  • C−2−6
  • D−5−2
  • E−2−5

Write a vector to represent the translation from Shape B to Shape C.

  • A−34
  • B−43
  • C26
  • D−2−6
  • E3−4

Write a vector to represent the translation from Shape C to Shape A.

  • A−2−6
  • B26
  • C62
  • D3−4
  • E−34

Q3:

Consider triangle 𝐴𝐵𝐶,where its vertices are at 𝐴=87, 𝐵=127, and 𝐶=129. If the triangle is translated by a vector V=−2−3, what are the coordinates of its image 𝐴𝐵𝐶?

  • A𝐴=87, 𝐵=127, and 𝐶=−2−3
  • B𝐴=64, 𝐵=106, and 𝐶=104
  • C𝐴=64, 𝐵=104, and 𝐶=106
  • D𝐴=610, 𝐵=410, and 𝐶=106
  • E𝐴=64, 𝐵=44, and 𝐶=410

Q4:

Use the translation vector V=1−2 to find the image of the point 85.

  • A9−3
  • B77
  • C93
  • D85
  • E−7−7

Q5:

Consider square 𝐴𝐵𝐶𝐷, where 𝐴56, 𝐵36, 𝐶37, and 𝐷57. Find the coordinates of 𝐷′ of the image 𝐴′𝐵′𝐶′𝐷′ after the translation with −11.

  • A84
  • B75
  • C56
  • D48
  • E−4−8

Q6:

Consider triangle 𝐴𝐵𝐶, where 𝐴=53, 𝐵=73, and 𝐶=75. If the triangle is translated by a vector V=1−5, which of the following is true?

  • ATriangle 𝐴𝐵𝐶 is translated by 1 units to the left and 5 units down.
  • BTriangle 𝐴𝐵𝐶 is translated by 1 units to the right and 5 units down.
  • CTriangle 𝐴𝐵𝐶 is translated by 1 units to the right and 5 units up.
  • DTriangle 𝐴𝐵𝐶 is translated by 5 units to the left and 1 units up.
  • ETriangle 𝐴𝐵𝐶 is translated by 5 units to the right and 1 units down.

Q7:

Which of the following vectors defines the translation that happens to square 𝐴𝐵𝐶𝐷?

  • A−11
  • B11
  • C2−2
  • D−1−1
  • E1−1

Q8:

Which of the following vectors defines the translation that occurs to the red triangle?

  • A22
  • B1−1
  • C−11
  • D11
  • E2−1

Q9:

The red triangle is the image of the blue triangle after a translation. Which vector describes the translation?

  • A(−4,2)
  • B(−2,4)
  • C(4,2)
  • D(2,−4)
  • E(4,−2)

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