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)

Q11:

What translation moves point 𝐴 to point 𝐡?

  • AThe translation of three left and three up
  • BThe translation of three right and three up
  • CThe translation of four left and four down
  • DThe translation of three left and three down
  • EThe translation of three right and three down

Q12:

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

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

Q13:

A translation maps a point two right and four down. Which of the following functions represents this transformation applied to a general point (π‘₯,𝑦)?

  • A(π‘₯,𝑦)β†’(2,βˆ’4)
  • B(π‘₯,𝑦)β†’(π‘₯βˆ’2,𝑦+4)
  • C(π‘₯,𝑦)β†’(π‘₯+2,π‘¦βˆ’4)
  • D(π‘₯,𝑦)β†’(βˆ’2,4)
  • E(π‘₯,𝑦)β†’(π‘₯+2,𝑦+4)

Q14:

In the given figure, 𝐴 has been translated to 𝐡. What function would describe this transformation?

  • A(π‘₯,𝑦)β†’(π‘₯+6,2)
  • B(π‘₯,𝑦)β†’(π‘₯+6,𝑦+2)
  • C(π‘₯,𝑦)β†’(π‘₯+4,𝑦+2)
  • D(π‘₯,𝑦)β†’(π‘₯+4,π‘¦βˆ’2)
  • E(π‘₯,𝑦)β†’(π‘₯+6,π‘¦βˆ’2)

Q15:

The points (8,12), (10,7), (13,14), (15,9) are moved down by 7 units. What are the new coordinates?

  • A(8,5), (10,0), (13,7), (15,2)
  • B(8,19), (10,14), (13,21), (15,16)
  • C(15,12), (17,7), (20,14), (22,9)
  • D(1,5), (3,0), (6,7), (8,2)
  • E(1,12), (3,7), (6,14), (8,9)

Q16:

The coordinates of point 𝐴 and its image 𝐴′ after a translation are illustrated in the graph below. Describe this translation in words.

  • A12 units left and 4 units up
  • B12 units right and 4 units down
  • C12 units right and 4 units up
  • D4 units right and 12 units up
  • E12 units left and 4 units down

Q17:

Determine the image of the two points 𝐴(βˆ’2,βˆ’6) and 𝐡(3,βˆ’7) under the translation (3,3).

  • A𝐴′(βˆ’3,1), 𝐡′(βˆ’4,6)
  • B𝐴′(1,βˆ’3), 𝐡′(βˆ’4,6)
  • C𝐴′(1,βˆ’3), 𝐡′(6,βˆ’4)
  • D𝐴′(βˆ’3,1), 𝐡′(6,βˆ’4)

Q18:

Find the images of the points 𝐴 and 𝐡 of the line segment 𝐴𝐡 under the translation (4,3).

  • A𝐴′(βˆ’3,2), 𝐡′(βˆ’1,5)
  • B𝐴′(2,βˆ’3), 𝐡′(5,βˆ’1)
  • C𝐴′(1,βˆ’2), 𝐡′(4,0)
  • D𝐴′(4,3), 𝐡′(5,βˆ’1)

Q19:

In the figure below, determine the coordinates of the points 𝐴′, 𝐡′, 𝐢′, and 𝐷′, where 𝐴′𝐡′𝐢′𝐷′ is a translation of 𝐴𝐡𝐢𝐷 by (βˆ’2,βˆ’5).

  • A𝐴′(1,6), 𝐡′(βˆ’4,6), 𝐢′(βˆ’4,βˆ’1), 𝐷′(βˆ’1,1)
  • B𝐴′(6,0), 𝐡′(6,βˆ’5), 𝐢′(βˆ’1,βˆ’5), 𝐷′(1,βˆ’2)
  • C𝐴′(7,1), 𝐡′(7,βˆ’4), 𝐢′(0,βˆ’4), 𝐷′(2,βˆ’1)
  • D𝐴′(6,1), 𝐡′(6,βˆ’4), 𝐢′(βˆ’1,βˆ’4), 𝐷′(1,βˆ’1)
  • E𝐴′(3,4), 𝐡′(3,βˆ’1), 𝐢′(βˆ’4,βˆ’1), 𝐷′(βˆ’2,2)

Q20:

Find the coordinates of the image of (13,4) under the translation (π‘₯,𝑦)β†’(π‘₯+5,π‘¦βˆ’2).

  • A(13,βˆ’4)
  • B(18,2)
  • C(8,6)
  • D(βˆ’8,βˆ’6)
  • E(βˆ’13,βˆ’4)

Q21:

Given that the translation of point 𝐴 by (βˆ’9,7) is 𝐴′(βˆ’1,2), find the coordinates of 𝐴.

  • A(βˆ’5,8)
  • B(βˆ’1,2)
  • C(βˆ’9,7)
  • D(8,βˆ’5)

Q22:

Find the image of the point 𝐴(βˆ’7,12) under a translation of 13 units in the negative direction of the π‘₯-axis.

  • A𝐴′(βˆ’20,βˆ’1)
  • B𝐴′(βˆ’7,βˆ’1)
  • C𝐴′(βˆ’20,12)
  • D𝐴′(6,12)

Q23:

A table has the coordinates (6,2), (13,2), (13,14), and (6,14). Each unit represents (6,2) feet. If the table is moved 2 feet to the left and 4feetup, determine its new location.

  • A(8,6), (15,6), (15,18), (8,18)
  • B(8,βˆ’2), (15,βˆ’2), (15,10), (8,10)
  • C(10,0), (17,0), (17,12), (10,12)
  • D(2,4), (9,4), (9,16), (2,16)
  • E(4,6), (11,6), (11,18), (4,18)

Q24:

If the image of the point 𝐴(9,8) by translation in the Cartesian plane is 𝐴′(19,βˆ’1), find the rule of the translation.

  • A(π‘₯,𝑦)⟢(π‘₯+10,π‘¦βˆ’9)
  • B(π‘₯,𝑦)⟢(π‘₯βˆ’9,𝑦+10)
  • C(π‘₯,𝑦)⟢(π‘₯βˆ’10,𝑦+9)
  • D(π‘₯,𝑦)⟢(π‘₯+28,𝑦+7)

Q25:

The point 𝐴(βˆ’4,βˆ’8) is translated one unit down to the point 𝐴′. What are the coordinates of 𝐴′?

  • A(βˆ’4,βˆ’7)
  • B(βˆ’5,βˆ’9)
  • C(βˆ’5,βˆ’8)
  • D(βˆ’9,βˆ’4)
  • E(βˆ’4,βˆ’9)

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