Lesson Worksheet: Translations on a Coordinate Plane Mathematics • 8th Grade

In this worksheet, we will practice applying the concept of translation to a point or a geometric shape and determining the coordinates of a translated image on the xy-plane.

Q1:

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)

Q2:

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)

Q3:

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)

Q4:

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)

Q5:

Find the image of a △𝐴𝐡𝐢, where the coordinates of 𝐴, 𝐡, and 𝐢 are (βˆ’7,βˆ’7), (4,βˆ’7), and (2,1), respectively, under the translation (3,2).

  • A𝐴′(βˆ’5,βˆ’4), 𝐡′(βˆ’5,7), 𝐢′(5,3)
  • B𝐴′(βˆ’4,βˆ’5), 𝐡′(7,βˆ’5), 𝐢′(5,3)
  • C𝐴′(βˆ’5,βˆ’4), 𝐡′(7,βˆ’5), 𝐢′(5,3)
  • D𝐴′(βˆ’4,βˆ’5), 𝐡′(7,βˆ’5), 𝐢′(3,5)
  • E𝐴′(βˆ’4,βˆ’5), 𝐡′(βˆ’5,7), 𝐢′(5,3)

Q6:

Find the coordinates of the point (π‘₯,𝑦) after it is translated π‘š units left and 𝑛 units down.

  • A(π‘₯+π‘š,𝑦+𝑛)
  • B(π‘₯βˆ’π‘š,π‘¦βˆ’π‘›)
  • C(π‘₯βˆ’π‘›,π‘¦βˆ’π‘š)
  • D(π‘₯+𝑛,𝑦+π‘š)
  • E(π‘₯βˆ’π‘š,𝑦+𝑛)

Q7:

The vertices of a triangle are mapped using the function (π‘₯,𝑦)β†’(π‘₯βˆ’2,𝑦+3). Which of the following single transformations has taken place?

  • Ahorizontal stretching
  • Btranslation
  • Creflection
  • Drotation

Q8:

What is the translation that will move point 𝐡 to point 𝐴?

  • AA translation of three right and three up
  • BA translation of three right and three down
  • CA translation of three left and three down
  • DA translation of three left and three up
  • EA translation of four left and four up

Q9:

A figure has been translated three right and two down and then translated a further eight right and six up. What single transformation could have been used?

  • Aa translation of ten right and eight down
  • Ba translation of eleven right and eight up
  • Ca translation of eleven right and four up
  • Da translation of eleven left and eight down
  • Ea translation of twelve right and nine up

Q10:

If a point with coordinates (π‘₯,𝑦) is translated three right and two down, determine the coordinates of the image.

  • A(π‘₯βˆ’2,𝑦+3)
  • B(π‘₯βˆ’3,𝑦+2)
  • C(π‘₯+2,π‘¦βˆ’3)
  • D(π‘₯+3,π‘¦βˆ’2)
  • E(π‘₯+3,𝑦+2)

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