Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
Homework Help
Start Practicing

Worksheet: Finding 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:

Write the translation that takes point 𝐴 to point 𝐴 β€² .

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

Q2:

Write the translation that takes point 𝐴 to point 𝐴 β€² .

  • A ( 2 , 3 )
  • B ( βˆ’ 2 , βˆ’ 3 )
  • C ( 2 , βˆ’ 3 )
  • D ( βˆ’ 2 , 3 )
  • E ( 3 , βˆ’ 2 )

Q3:

Write the translation that takes point 𝐴 to point 𝐴 β€² .

  • A ( 1 2 , 7 )
  • B ( βˆ’ 1 2 , βˆ’ 7 )
  • C ( 1 2 , βˆ’ 7 )
  • D ( βˆ’ 1 2 , 7 )
  • E ( 7 , βˆ’ 1 2 )

Q4:

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

  • A 𝐴 β€² ( 1 , βˆ’ 3 ) , 𝐡 β€² ( βˆ’ 4 , 6 )
  • B 𝐴 β€² ( βˆ’ 3 , 1 ) , 𝐡 β€² ( 6 , βˆ’ 4 )
  • C 𝐴 β€² ( βˆ’ 3 , 1 ) , 𝐡 β€² ( βˆ’ 4 , 6 )
  • D 𝐴 β€² ( 1 , βˆ’ 3 ) , 𝐡 β€² ( 6 , βˆ’ 4 )

Q5:

Determine the image of the two points 𝐴 ( βˆ’ 7 , βˆ’ 3 ) and 𝐡 ( 4 , βˆ’ 5 ) under the translation ( 2 , 4 ) .

  • A 𝐴 β€² ( βˆ’ 5 , 1 ) , 𝐡 β€² ( βˆ’ 1 , 6 )
  • B 𝐴 β€² ( 1 , βˆ’ 5 ) , 𝐡 β€² ( 6 , βˆ’ 1 )
  • C 𝐴 β€² ( 1 , βˆ’ 5 ) , 𝐡 β€² ( βˆ’ 1 , 6 )
  • D 𝐴 β€² ( βˆ’ 5 , 1 ) , 𝐡 β€² ( 6 , βˆ’ 1 )

Q6:

Determine the image of the two points 𝐴 ( βˆ’ 3 , βˆ’ 3 ) and 𝐡 ( 3 , βˆ’ 5 ) under the translation ( 2 , 9 ) .

  • A 𝐴 β€² ( βˆ’ 1 , 6 ) , 𝐡 β€² ( 4 , 5 )
  • B 𝐴 β€² ( 6 , βˆ’ 1 ) , 𝐡 β€² ( 5 , 4 )
  • C 𝐴 β€² ( 6 , βˆ’ 1 ) , 𝐡 β€² ( 4 , 5 )
  • D 𝐴 β€² ( βˆ’ 1 , 6 ) , 𝐡 β€² ( 5 , 4 )

Q7:

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

  • A 𝐴 β€² ( 1 , βˆ’ 2 ) , 𝐡 β€² ( 4 , 0 )
  • B 𝐴 β€² ( βˆ’ 3 , 2 ) , 𝐡 β€² ( βˆ’ 1 , 5 )
  • C 𝐴 β€² ( 4 , 3 ) , 𝐡 β€² ( 5 , βˆ’ 1 )
  • D 𝐴 β€² ( 2 , βˆ’ 3 ) , 𝐡 β€² ( 5 , βˆ’ 1 )

Q8:

Find the images of the points 𝐴 and 𝐡 of the line segment 𝐴 𝐡 under the translation ( 4 , 5 ) .

  • A 𝐴 β€² ( βˆ’ 2 , 1 ) , 𝐡 β€² ( 7 , 6 )
  • B 𝐴 β€² ( 2 , βˆ’ 3 ) , 𝐡 β€² ( 7 , 6 )
  • C 𝐴 β€² ( 4 , 5 ) , 𝐡 β€² ( 6 , 7 )
  • D 𝐴 β€² ( βˆ’ 3 , 2 ) , 𝐡 β€² ( 6 , 7 )

Q9:

Find the images of the points 𝐴 and 𝐡 of the line segment 𝐴 𝐡 under the translation ( 5 , βˆ’ 2 ) .

  • A 𝐴 β€² ( βˆ’ 7 , 8 ) , 𝐡 β€² ( βˆ’ 1 , 1 2 )
  • B 𝐴 β€² ( 1 , 0 ) , 𝐡 β€² ( 5 , 6 )
  • C 𝐴 β€² ( 5 , βˆ’ 2 ) , 𝐡 β€² ( 6 , 5 )
  • D 𝐴 β€² ( 0 , 1 ) , 𝐡 β€² ( 6 , 5 )

Q10:

In the figure below, determine the coordinates of the points 𝐴 β€² , 𝐡 β€² , 𝐢 β€² , and 𝐷 β€² , where 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² is a translation of 𝐴 𝐡 𝐢 𝐷 by ( βˆ’ 1 , βˆ’ 2 ) .

  • A 𝐴 β€² ( 4 , 4 ) , 𝐡 β€² ( βˆ’ 1 , 5 ) , 𝐢 β€² ( βˆ’ 1 , 1 ) , 𝐷 β€² ( 2 , 0 )
  • B 𝐴 β€² ( 5 , 4 ) , 𝐡 β€² ( 6 , βˆ’ 1 ) , 𝐢 β€² ( 2 , βˆ’ 1 ) , 𝐷 β€² ( 1 , 2 )
  • C 𝐴 β€² ( 3 , 5 ) , 𝐡 β€² ( 4 , 0 ) , 𝐢 β€² ( 0 , 0 ) , 𝐷 β€² ( βˆ’ 1 , 3 )
  • D 𝐴 β€² ( 4 , 4 ) , 𝐡 β€² ( 5 , βˆ’ 1 ) , 𝐢 β€² ( 1 , βˆ’ 1 ) , 𝐷 β€² ( 0 , 2 )
  • E 𝐴 β€² ( 4 , 3 ) , 𝐡 β€² ( 5 , βˆ’ 2 ) , 𝐢 β€² ( 1 , βˆ’ 2 ) , 𝐷 β€² ( 0 , 1 )

Q11:

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

  • A 𝐴 β€² ( 1 , 6 ) , 𝐡 β€² ( βˆ’ 4 , 6 ) , 𝐢 β€² ( βˆ’ 4 , βˆ’ 1 ) , 𝐷 β€² ( βˆ’ 1 , 1 )
  • B 𝐴 β€² ( 7 , 1 ) , 𝐡 β€² ( 7 , βˆ’ 4 ) , 𝐢 β€² ( 0 , βˆ’ 4 ) , 𝐷 β€² ( 2 , βˆ’ 1 )
  • C 𝐴 β€² ( 3 , 4 ) , 𝐡 β€² ( 3 , βˆ’ 1 ) , 𝐢 β€² ( βˆ’ 4 , βˆ’ 1 ) , 𝐷 β€² ( βˆ’ 2 , 2 )
  • D 𝐴 β€² ( 6 , 1 ) , 𝐡 β€² ( 6 , βˆ’ 4 ) , 𝐢 β€² ( βˆ’ 1 , βˆ’ 4 ) , 𝐷 β€² ( 1 , βˆ’ 1 )
  • E 𝐴 β€² ( 6 , 0 ) , 𝐡 β€² ( 6 , βˆ’ 5 ) , 𝐢 β€² ( βˆ’ 1 , βˆ’ 5 ) , 𝐷 β€² ( 1 , βˆ’ 2 )

Q12:

In the figure below, determine the coordinates of the points 𝐴 β€² , 𝐡 β€² , 𝐢 β€² , and 𝐷 β€² , where 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² is a translation of 𝐴 𝐡 𝐢 𝐷 by ( 1 , βˆ’ 5 ) .

  • A 𝐴 β€² ( βˆ’ 3 , 3 ) , 𝐡 β€² ( βˆ’ 8 , 2 ) , 𝐢 β€² ( βˆ’ 7 , βˆ’ 3 ) , 𝐷 β€² ( βˆ’ 4 , βˆ’ 1 )
  • B 𝐴 β€² ( 4 , βˆ’ 3 ) , 𝐡 β€² ( 3 , βˆ’ 8 ) , 𝐢 β€² ( βˆ’ 2 , βˆ’ 7 ) , 𝐷 β€² ( 0 , βˆ’ 4 )
  • C 𝐴 β€² ( βˆ’ 3 , 3 ) , 𝐡 β€² ( βˆ’ 4 , βˆ’ 2 ) , 𝐢 β€² ( βˆ’ 9 , βˆ’ 1 ) , 𝐷 β€² ( βˆ’ 7 , 2 )
  • D 𝐴 β€² ( 3 , βˆ’ 3 ) , 𝐡 β€² ( 2 , βˆ’ 8 ) , 𝐢 β€² ( βˆ’ 3 , βˆ’ 7 ) , 𝐷 β€² ( βˆ’ 1 , βˆ’ 4 )
  • E 𝐴 β€² ( 3 , βˆ’ 4 ) , 𝐡 β€² ( 2 , βˆ’ 9 ) , 𝐢 β€² ( βˆ’ 3 , βˆ’ 8 ) , 𝐷 β€² ( βˆ’ 1 , βˆ’ 5 )

Q13:

Find the coordinates of the image of ( 1 3 , 4 ) under the translation ( π‘₯ , 𝑦 ) β†’ ( π‘₯ + 5 , 𝑦 βˆ’ 2 ) .

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

Q14:

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

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

Q15:

Find the image of the point 𝐴 ( βˆ’ 7 , 1 2 ) under a translation of 13 units in the negative direction of the π‘₯ -axis.

  • A 𝐴 β€² ( βˆ’ 7 , βˆ’ 1 )
  • B 𝐴 β€² ( 6 , 1 2 )
  • C 𝐴 β€² ( βˆ’ 2 0 , βˆ’ 1 )
  • D 𝐴 β€² ( βˆ’ 2 0 , 1 2 )

Q16:

An angle with a measure of 4 5 ∘ is translated three left and eight up. What is the measure of its image?

Q17:

A table has the coordinates ( 6 , 2 ) , ( 1 3 , 2 ) , ( 1 3 , 1 4 ) , and ( 6 , 1 4 ) . Each unit represents (6, 2) feet. If the table is moved 2 feet to the left and 4 f e e t u p , determine its new location.

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

Q18:

If the image of the point 𝐴 ( 9 , 8 ) by translation in the Cartesian plane is 𝐴 β€² ( 1 9 , βˆ’ 1 ) , find the rule of the translation.

  • A ( π‘₯ , 𝑦 ) ⟢ ( π‘₯ βˆ’ 9 , 𝑦 + 1 0 )
  • B ( π‘₯ , 𝑦 ) ⟢ ( π‘₯ βˆ’ 1 0 , 𝑦 + 9 )
  • C ( π‘₯ , 𝑦 ) ⟢ ( π‘₯ + 2 8 , 𝑦 + 7 )
  • D ( π‘₯ , 𝑦 ) ⟢ ( π‘₯ + 1 0 , 𝑦 βˆ’ 9 )

Q19:

Given that 𝐴 β€² is the image of point 𝐴 ( βˆ’ 4 , βˆ’ 8 ) by translation of magnitude of 1unit in the negative direction of the 𝑦 -axis, what are the coordinates of 𝐴 β€² ?

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

Q20:

Three points 𝐴 , 𝐡 , and 𝐢 with coordinates (1, 3), (1, 2), and (4, 1), respectively, are translated three left and four up to the points 𝐴 β€² , 𝐡 β€² , and 𝐢 β€² .

Determine the coordinates of 𝐴 β€² , 𝐡 β€² , and 𝐢 β€² .

  • A 𝐴 β€² = ( 1 , 7 ) , 𝐡 β€² = ( 1 , 6 ) , and 𝐢 β€² = ( 4 , 5 )
  • B 𝐴 β€² = ( βˆ’ 2 , 3 ) , 𝐡 β€² = ( βˆ’ 2 , 2 ) , and 𝐢 β€² = ( 1 , 1 )
  • C 𝐴 β€² = ( 7 , βˆ’ 2 ) , 𝐡 β€² = ( 6 , βˆ’ 2 ) , and 𝐢 β€² = ( 5 , 1 )
  • D 𝐴 β€² = ( βˆ’ 2 , 7 ) , 𝐡 β€² = ( βˆ’ 2 , 6 ) , and 𝐢 β€² = ( 1 , 5 )
  • E 𝐴 β€² = ( 5 , 0 ) , 𝐡 β€² = ( 5 , βˆ’ 1 ) , and 𝐢 β€² = ( 8 , βˆ’ 2 )

Is the measure of angle 𝐴 𝐡 𝐢 less than, greater than, or equal to the measure of angle 𝐴 β€² 𝐡 β€² 𝐢 β€² ?

  • Aequal to
  • Bgreater than
  • Cless than

Q21:

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

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

Q22:

The two triangles and in the given figure are congruent. Select the congruence transformation that could have been used to map triangle to .

  • A a reflection about the -axis
  • B a rotation counterclockwise about the point
  • C a reflection about the -axis
  • D a translation 6 right and 4 down
  • Ea translation 4 right and 2 down

Q23:

Draw the rectangle 𝐴 𝐡 𝐢 𝐷 , where the coordinates of the points 𝐴 , 𝐡 , 𝐢 , and 𝐷 are ( βˆ’ 5 , 0 ) , ( βˆ’ 2 , 0 ) , ( βˆ’ 2 , 2 ) , and ( βˆ’ 5 , 2 ) , respectively, and find its image under the translation ( βˆ’ 1 0 , βˆ’ 4 ) .

  • A 𝐴 β€² ( 5 , 4 ) , 𝐡 β€² ( 8 , 4 ) , 𝐢 β€² ( 8 , 6 ) , 𝐷 β€² ( 5 , 6 )
  • B 𝐴 β€² ( βˆ’ 4 , βˆ’ 1 5 ) , 𝐡 β€² ( βˆ’ 4 , βˆ’ 1 2 ) , 𝐢 β€² ( βˆ’ 2 , βˆ’ 1 2 ) , 𝐷 β€² ( βˆ’ 2 , βˆ’ 1 5 )
  • C 𝐴 β€² ( 1 5 , 4 ) , 𝐡 β€² ( 1 2 , 4 ) , 𝐢 β€² ( 1 2 , 2 ) , 𝐷 β€² ( 1 5 , 2 )
  • D 𝐴 β€² ( βˆ’ 1 5 , βˆ’ 4 ) , 𝐡 β€² ( βˆ’ 1 2 , βˆ’ 4 ) , 𝐢 β€² ( βˆ’ 1 2 , βˆ’ 2 ) , 𝐷 β€² ( βˆ’ 1 5 , βˆ’ 2 )

Q24:

Determine the image of the point 𝐴 ( 0 , 7 ) under the translation ( 1 , βˆ’ 4 ) .

  • A ( 1 , βˆ’ 4 )
  • B ( βˆ’ 4 , 8 )
  • C ( βˆ’ 1 , 1 1 )
  • D ( 1 , 3 )

Q25:

If and are two points in the Cartesian plane, write the mapping rule of the translation that makes the image of .

  • A
  • B
  • C
  • D

Related Lessons

Related Videos

Related Worksheets