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(14,11)
  • C(12,13)
  • D(11,14)
  • E(11,14)

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).

  • A𝐴(5,4), 𝐵(5,7), 𝐶(5,3)
  • B𝐴(4,5), 𝐵(7,5), 𝐶(5,3)
  • C𝐴(5,4), 𝐵(7,5), 𝐶(5,3)
  • D𝐴(4,5), 𝐵(7,5), 𝐶(3,5)
  • E𝐴(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(𝑥𝑚,𝑦𝑛)
  • C(𝑥𝑛,𝑦𝑚)
  • D(𝑥+𝑛,𝑦+𝑚)
  • E(𝑥𝑚,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(𝑥2,𝑦+3)
  • B(𝑥3,𝑦+2)
  • C(𝑥+2,𝑦3)
  • D(𝑥+3,𝑦2)
  • 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(𝑥𝑛,𝑦𝑚)
  • B(𝑥+𝑚,𝑦𝑛)
  • C(𝑥𝑚,𝑦𝑛)
  • 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)(𝑥2,𝑦+4)
  • C(𝑥,𝑦)(𝑥+2,𝑦4)
  • 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,𝑦2)
  • E(𝑥,𝑦)(𝑥+6,𝑦2)

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(2,6) and 𝐵(3,7) under the translation (3,3).

  • A𝐴(3,1), 𝐵(4,6)
  • B𝐴(1,3), 𝐵(4,6)
  • C𝐴(1,3), 𝐵(6,4)
  • D𝐴(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).

  • A𝐴(3,2), 𝐵(1,5)
  • B𝐴(2,3), 𝐵(5,1)
  • C𝐴(1,2), 𝐵(4,0)
  • D𝐴(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).

  • A𝐴(1,6), 𝐵(4,6), 𝐶(4,1), 𝐷(1,1)
  • B𝐴(6,0), 𝐵(6,5), 𝐶(1,5), 𝐷(1,2)
  • C𝐴(7,1), 𝐵(7,4), 𝐶(0,4), 𝐷(2,1)
  • D𝐴(6,1), 𝐵(6,4), 𝐶(1,4), 𝐷(1,1)
  • E𝐴(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(13,4)
  • B(18,2)
  • C(8,6)
  • D(8,6)
  • E(13,4)

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.

  • A𝐴(20,1)
  • B𝐴(7,1)
  • C𝐴(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(8,2), (15,2), (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(19,1), find the rule of the translation.

  • A(𝑥,𝑦)(𝑥+10,𝑦9)
  • B(𝑥,𝑦)(𝑥9,𝑦+10)
  • C(𝑥,𝑦)(𝑥10,𝑦+9)
  • D(𝑥,𝑦)(𝑥+28,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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