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 , 5 )
  • B ( 3 , 2 )
  • C ( 0 , 7 )
  • D ( 6 , 2 )
  • E ( 6 , 8 )

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

Q3:

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

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

Q4:

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

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

Q5:

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

  • A 𝐴 ′ ( − 4 , − 5 ) , 𝐵 ′ ( − 5 , 7 ) , 𝐶 ′ ( 5 , 3 )
  • B 𝐴 ′ ( − 5 , − 4 ) , 𝐵 ′ ( 7 , − 5 ) , 𝐶 ′ ( 5 , 3 )
  • C 𝐴 ′ ( − 4 , − 5 ) , 𝐵 ′ ( 7 , − 5 ) , 𝐶 ′ ( 3 , 5 )
  • D 𝐴 ′ ( − 4 , − 5 ) , 𝐵 ′ ( 7 , − 5 ) , 𝐶 ′ ( 5 , 3 )
  • E 𝐴 ′ ( − 5 , − 4 ) , 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 − 𝑛 , 𝑦 − 𝑚 )
  • B ( 𝑥 + 𝑚 , 𝑦 + 𝑛 )
  • C ( 𝑥 + 𝑛 , 𝑦 + 𝑚 )
  • D ( 𝑥 − 𝑚 , 𝑦 − 𝑛 )
  • E ( 𝑥 − 𝑚 , 𝑦 + 𝑛 )

Q7:

If triangle 𝑇 is mapped to triangle 𝑇 ′ by a translation, would the corresponding angles and sides in the triangle be equal?

  • A yes
  • B no

Q8:

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?

  • Areflection
  • Brotation
  • Chorizontal stretching
  • Dtranslation

Q9:

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

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

Q10:

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?

  • A a translation of ten right and eight down
  • B a translation of eleven right and eight up
  • C a translation of eleven left and eight down
  • D a translation of eleven right and four up
  • Ea translation of twelve right and nine up

Q11:

What is the name of the transformation that slides figures without flipping or rotating them?

  • Areflection
  • Brotation
  • Cdilation
  • Dtranslation
  • Ehorizontal stretching

Q12:

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

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

Q13:

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

Q14:

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

Q15:

Farida wants to change the location of her right-triangular desk. If she moves it only by a translation, will it fit exactly into one of the other corners of the room?

  • A no
  • B yes

Q16:

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

Q17:

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

  • A ( 𝑥 , 𝑦 ) → ( 𝑥 + 4 , 𝑦 − 2 )
  • B ( 𝑥 , 𝑦 ) → ( 𝑥 + 4 , 𝑦 + 2 )
  • C ( 𝑥 , 𝑦 ) → ( 𝑥 + 6 , 𝑦 − 2 )
  • D ( 𝑥 , 𝑦 ) → ( 𝑥 + 6 , 𝑦 + 2 )
  • E ( 𝑥 , 𝑦 ) → ( 𝑥 + 6 , 2 )

Q18:

The points ( 8 , 1 2 ) , ( 1 0 , 7 ) , ( 1 3 , 1 4 ) , ( 1 5 , 9 ) are moved down by 7 units. What are the new coordinates?

  • A ( 1 , 1 2 ) , ( 3 , 7 ) , ( 6 , 1 4 ) , ( 8 , 9 )
  • 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 ( 8 , 5 ) , ( 1 0 , 0 ) , ( 1 3 , 7 ) , ( 1 5 , 2 )
  • E ( 1 , 5 ) , ( 3 , 0 ) , ( 6 , 7 ) , ( 8 , 2 )

Q19:

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 right and 4 units down
  • B4 units right and 12 units up
  • C12 units left and 4 units up
  • D12 units right and 4 units up
  • E12 units left and 4 units down

Q20:

Determine the image of the two points 𝐴 ( − 2 , − 6 ) and 𝐵 ( 3 , − 7 ) under the translation ( 3 , 3 ) .

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

Q21:

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

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

Q22:

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

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

Q23:

Find the coordinates of the image of ( 1 3 , 4 ) under the translation ( 𝑥 , 𝑦 ) → ( 𝑥 + 5 , 𝑦 − 2 ) .

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

Q24:

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

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

Q25:

Find the image of the point 𝐴 ( − 7 , 1 2 ) under a translation of 13 units in the negative direction of the 𝑥 -axis.

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

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