Worksheet: Translations on a Coordinate Plane

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)(𝑥2,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 𝐴𝐵𝐶𝐷 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,𝑦2).

  • 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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