Worksheet: Translations on a Coordinate Plane

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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(−5,−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 ( − 8 , 8 )
  • C ( 1 , − 1 )
  • D ( − 5 , 5 )
  • E ( 2 , 8 )

Q3:

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

  • A ( − 4 , − 5 )
  • B ( − 1 4 , − 1 1 )
  • C ( − 1 2 , − 1 3 )
  • D ( 1 1 , 1 4 )
  • E ( − 1 1 , − 1 4 )

Q4:

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

  • A ( − 9 , − 7 )
  • B ( 7 , − 9 )
  • C ( − 7 , − 9 )
  • D ( − 7 , 9 )
  • E ( 7 , 9 )

Q5:

Find the image of a △𝐴𝐵𝐶, where the coordinates of 𝐴, 𝐵, and 𝐶 are (−7,−7), (4,−7), and (2,1), respectively, under the translation (3,2).

  • A 𝐴 ′ ( − 5 , − 4 ) , 𝐵 ′ ( − 5 , 7 ) , 𝐶 ′ ( 5 , 3 )
  • B 𝐴 ′ ( − 4 , − 5 ) , 𝐵 ′ ( 7 , − 5 ) , 𝐶 ′ ( 5 , 3 )
  • C 𝐴 ′ ( − 5 , − 4 ) , 𝐵 ′ ( 7 , − 5 ) , 𝐶 ′ ( 5 , 3 )
  • D 𝐴 ′ ( − 4 , − 5 ) , 𝐵 ′ ( 7 , − 5 ) , 𝐶 ′ ( 3 , 5 )
  • E 𝐴 ′ ( − 4 , − 5 ) , 𝐵 ′ ( − 5 , 7 ) , 𝐶 ′ ( 5 , 3 )

Q6:

Find the coordinates of the point (𝑥,𝑦) after it is translated 𝑚 units left and 𝑛 units down.

  • A ( 𝑥 + 𝑚 , 𝑦 + 𝑛 )
  • B ( 𝑥 − 𝑚 , 𝑦 − 𝑛 )
  • C ( 𝑥 − 𝑛 , 𝑦 − 𝑚 )
  • D ( 𝑥 + 𝑛 , 𝑦 + 𝑚 )
  • E ( 𝑥 − 𝑚 , 𝑦 + 𝑛 )

Q7:

The vertices of a triangle are mapped using the function (𝑥,𝑦)→(𝑥−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 𝐵 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 (𝑥,𝑦) is translated three right and two down, determine the coordinates of the image.

  • A ( 𝑥 − 2 , 𝑦 + 3 )
  • B ( 𝑥 − 3 , 𝑦 + 2 )
  • C ( 𝑥 + 2 , 𝑦 − 3 )
  • D ( 𝑥 + 3 , 𝑦 − 2 )
  • E ( 𝑥 + 3 , 𝑦 + 2 )

Q11:

What translation moves point 𝐴 to point 𝐵?

  • 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 (𝑥,𝑦) after it is translated 𝑚 units right and 𝑛 units up.

  • A ( 𝑥 − 𝑛 , 𝑦 − 𝑚 )
  • B ( 𝑥 + 𝑚 , 𝑦 − 𝑛 )
  • C ( 𝑥 − 𝑚 , 𝑦 − 𝑛 )
  • D ( 𝑥 + 𝑛 , 𝑦 + 𝑚 )
  • E ( 𝑥 + 𝑚 , 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 (𝑥,𝑦)?

  • A ( 𝑥 , 𝑦 ) → ( 2 , − 4 )
  • B ( 𝑥 , 𝑦 ) → ( 𝑥 − 2 , 𝑦 + 4 )
  • C ( 𝑥 , 𝑦 ) → ( 𝑥 + 2 , 𝑦 − 4 )
  • D ( 𝑥 , 𝑦 ) → ( − 2 , 4 )
  • E ( 𝑥 , 𝑦 ) → ( 𝑥 + 2 , 𝑦 + 4 )

Q14:

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

  • A ( 𝑥 , 𝑦 ) → ( 𝑥 + 6 , 2 )
  • B ( 𝑥 , 𝑦 ) → ( 𝑥 + 6 , 𝑦 + 2 )
  • C ( 𝑥 , 𝑦 ) → ( 𝑥 + 4 , 𝑦 + 2 )
  • D ( 𝑥 , 𝑦 ) → ( 𝑥 + 4 , 𝑦 − 2 )
  • E ( 𝑥 , 𝑦 ) → ( 𝑥 + 6 , 𝑦 − 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 ) , ( 1 0 , 0 ) , ( 1 3 , 7 ) , ( 1 5 , 2 )
  • B ( 8 , 1 9 ) , ( 1 0 , 1 4 ) , ( 1 3 , 2 1 ) , ( 1 5 , 1 6 )
  • C ( 1 5 , 1 2 ) , ( 1 7 , 7 ) , ( 2 0 , 1 4 ) , ( 2 2 , 9 )
  • D ( 1 , 5 ) , ( 3 , 0 ) , ( 6 , 7 ) , ( 8 , 2 )
  • E ( 1 , 1 2 ) , ( 3 , 7 ) , ( 6 , 1 4 ) , ( 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(−2,−6) and 𝐵(3,−7) under the translation (3,3).

  • A 𝐴 ′ ( − 3 , 1 ) , 𝐵 ′ ( − 4 , 6 )
  • B 𝐴 ′ ( 1 , − 3 ) , 𝐵 ′ ( − 4 , 6 )
  • C 𝐴 ′ ( 1 , − 3 ) , 𝐵 ′ ( 6 , − 4 )
  • D 𝐴 ′ ( − 3 , 1 ) , 𝐵 ′ ( 6 , − 4 )

Q18:

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

  • A 𝐴 ′ ( − 3 , 2 ) , 𝐵 ′ ( − 1 , 5 )
  • B 𝐴 ′ ( 2 , − 3 ) , 𝐵 ′ ( 5 , − 1 )
  • C 𝐴 ′ ( 1 , − 2 ) , 𝐵 ′ ( 4 , 0 )
  • D 𝐴 ′ ( 4 , 3 ) , 𝐵 ′ ( 5 , − 1 )

Q19:

In the figure below, determine the coordinates of the points 𝐴′, 𝐵′, 𝐶′, and 𝐷′, where 𝐴′𝐵′𝐶′𝐷′ is a translation of 𝐴𝐵𝐶𝐷 by (−2,−5).

  • A 𝐴 ′ ( 1 , 6 ) , 𝐵 ′ ( − 4 , 6 ) , 𝐶 ′ ( − 4 , − 1 ) , 𝐷 ′ ( − 1 , 1 )
  • B 𝐴 ′ ( 6 , 0 ) , 𝐵 ′ ( 6 , − 5 ) , 𝐶 ′ ( − 1 , − 5 ) , 𝐷 ′ ( 1 , − 2 )
  • C 𝐴 ′ ( 7 , 1 ) , 𝐵 ′ ( 7 , − 4 ) , 𝐶 ′ ( 0 , − 4 ) , 𝐷 ′ ( 2 , − 1 )
  • D 𝐴 ′ ( 6 , 1 ) , 𝐵 ′ ( 6 , − 4 ) , 𝐶 ′ ( − 1 , − 4 ) , 𝐷 ′ ( 1 , − 1 )
  • E 𝐴 ′ ( 3 , 4 ) , 𝐵 ′ ( 3 , − 1 ) , 𝐶 ′ ( − 4 , − 1 ) , 𝐷 ′ ( − 2 , 2 )

Q20:

Find the coordinates of the image of (13,4) under the translation (𝑥,𝑦)→(𝑥+5,𝑦−2).

  • A ( 1 3 , − 4 )
  • B ( 1 8 , 2 )
  • C ( 8 , 6 )
  • D ( − 8 , − 6 )
  • E ( − 1 3 , − 4 )

Q21:

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

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

Q22:

Find the image of the point 𝐴(−7,12) under a translation of 13 units in the negative direction of the 𝑥-axis.

  • A 𝐴 ′ ( − 2 0 , − 1 )
  • B 𝐴 ′ ( − 7 , − 1 )
  • C 𝐴 ′ ( − 2 0 , 1 2 )
  • D 𝐴 ′ ( 6 , 1 2 )

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 ) , ( 1 5 , 6 ) , ( 1 5 , 1 8 ) , ( 8 , 1 8 )
  • B ( 8 , − 2 ) , ( 1 5 , − 2 ) , ( 1 5 , 1 0 ) , ( 8 , 1 0 )
  • C ( 1 0 , 0 ) , ( 1 7 , 0 ) , ( 1 7 , 1 2 ) , ( 1 0 , 1 2 )
  • D ( 2 , 4 ) , ( 9 , 4 ) , ( 9 , 1 6 ) , ( 2 , 1 6 )
  • E ( 4 , 6 ) , ( 1 1 , 6 ) , ( 1 1 , 1 8 ) , ( 4 , 1 8 )

Q24:

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

  • A ( 𝑥 , 𝑦 ) ⟶ ( 𝑥 + 1 0 , 𝑦 − 9 )
  • B ( 𝑥 , 𝑦 ) ⟶ ( 𝑥 − 9 , 𝑦 + 1 0 )
  • C ( 𝑥 , 𝑦 ) ⟶ ( 𝑥 − 1 0 , 𝑦 + 9 )
  • D ( 𝑥 , 𝑦 ) ⟶ ( 𝑥 + 2 8 , 𝑦 + 7 )

Q25:

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

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

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