Lesson Worksheet: Translations on a Coordinate Plane Mathematics

In this worksheet, we will practice translating points, line segments, and shapes on the coordinate plane.


Write the translation that takes point 𝐴 to point 𝐴′.

  • A(βˆ’9,βˆ’7)
  • B(7,βˆ’9)
  • C(βˆ’7,βˆ’9)
  • D(βˆ’7,9)
  • E(7,9)


Determine the coordinates of the image of point 𝐡 of quadrilateral 𝐴𝐡𝐢𝐷 after a translation 5 units left and 3 units down.

  • A(βˆ’4,βˆ’5)
  • B(βˆ’14,βˆ’11)
  • C(βˆ’12,βˆ’13)
  • D(11,14)
  • E(βˆ’11,βˆ’14)


Start with point 𝐴(βˆ’5,βˆ’1). Translate it by 5 units to the left and 2 units up. Follow this with a translation of 5 units to the right and 4 units up. What are the new coordinates?

  • A(5,5)
  • B(βˆ’8,8)
  • C(1,βˆ’1)
  • D(βˆ’5,5)
  • E(2,8)


The point (3,5) has been translated three right and three down. What are the coordinates of the image?

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


In the given figure, which of the following transformations could be used to map the center of circle 𝐴 to the center of circle 𝐡?

  • A(π‘₯,𝑦)β†’(π‘₯+5,π‘¦βˆ’2)
  • B(π‘₯,𝑦)β†’(π‘₯βˆ’6,𝑦+2)
  • C(π‘₯,𝑦)β†’(π‘¦βˆ’2,π‘₯+6)
  • D(π‘₯,𝑦)β†’(π‘₯βˆ’5,𝑦+2)
  • E(π‘₯,𝑦)β†’(π‘₯+6,π‘¦βˆ’2)


Translate the given triangle using the function 𝑇(π‘₯,𝑦)β†’(π‘₯+2,π‘¦βˆ’2):. Which of the following sets of coordinates will be the vertices of the image?

  • A(βˆ’1,1),(βˆ’1,0), and (2,1)
  • B(1,1),(1,0), and (2,1)
  • C(βˆ’1,βˆ’1),(βˆ’1,0), and (2,βˆ’1)
  • D(1,βˆ’1),(0,βˆ’1), and (βˆ’1,βˆ’2)
  • E(βˆ’1,βˆ’1),(0,βˆ’1), and (βˆ’1,2)


If 𝐴𝐡𝐢 is a right triangle at 𝐡, where π‘šβˆ πΆ=43∘, and △𝐴′𝐡′𝐢′ is the image of △𝐴𝐡𝐢 by a translation of 4 cm in the direction of οƒͺ𝐢𝐡, find π‘šβˆ π΄π΄β€²πΆβ€² and π‘šβˆ πΆπ΄π΄β€².

  • Aπ‘šβˆ π΄π΄β€²πΆβ€²=47∘, π‘šβˆ πΆπ΄π΄β€²=133∘
  • Bπ‘šβˆ π΄π΄β€²πΆβ€²=47∘, π‘šβˆ πΆπ΄π΄β€²=137∘
  • Cπ‘šβˆ π΄π΄β€²πΆβ€²=43∘, π‘šβˆ πΆπ΄π΄β€²=133∘
  • Dπ‘šβˆ π΄π΄β€²πΆβ€²=43∘, π‘šβˆ πΆπ΄π΄β€²=137∘


In the figure, 𝐴𝐡 has been translated one right and three down. Is the length of the image resulting from this transformation greater than, less than, or the same as the length of 𝐴𝐡?

  • Agreater than
  • Bless than
  • Cthe same


Triangle 𝐴 has its vertices at (1,2), (1,5), and (3,2).

Select the figure which shows triangle 𝐴 and its image, 𝐡, after 𝐴 has been translated 3 units right and 6 units down.

  • A
  • B
  • C
  • D
  • E

Describe the translation which would take triangle 𝐡 back to triangle 𝐴.

  • A6 units left and 3 units up
  • B3 units left and 6 units down
  • C3 units left and 6 units up
  • D3 units right and 6 units down
  • E3 units right and 6 units up


Find the values of π‘Ž and 𝑏, given that the point (βˆ’2,βˆ’9) is the image of the point (βˆ’3,1) under the translation (π‘₯,𝑦)⟢(π‘₯+π‘Ž,𝑦+𝑏).

  • Aπ‘Ž=1, 𝑏=βˆ’10
  • Bπ‘Ž=βˆ’1, 𝑏=10
  • Cπ‘Ž=βˆ’1, 𝑏=βˆ’10
  • Dπ‘Ž=1, 𝑏=10

This lesson includes 23 additional questions and 207 additional question variations for subscribers.

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