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Worksheet: Reflections

In this worksheet, we will practice finding the images of points, lines, and shapes reflected in horizontal and vertical axes.

Q1:

If a point with coordinates ( π‘₯ , 𝑦 ) is reflected in the 𝑦 -axis, determine the coordinates of the image.

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

Q2:

If a point with coordinates ( π‘₯ , 𝑦 ) is reflected in the π‘₯ -axis, determine the coordinates of the image.

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

Q3:

What is the image of 𝐴 under reflection in the 𝑦 -axis?

  • A 𝐴 β€² ( 2 , βˆ’ 4 )
  • B 𝐴 β€² ( βˆ’ 2 , βˆ’ 4 )
  • C 𝐴 β€² ( 4 , 2 )
  • D 𝐴 β€² ( βˆ’ 2 , 4 )

Q4:

Given that 𝐴 β€² 𝐡 β€² is the image of 𝐴 𝐡 by reflection in the 𝑦 -axis, find the coordinates of the points 𝐴 β€² and 𝐡 β€² .

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

Q5:

What are the images of points 𝐴 and 𝐢 after a reflection in 𝐿 ?

  • A 𝐡 and 𝐢
  • B 𝐴 and 𝐡
  • C 𝐴 and 𝐢

Q6:

Find the images of 𝐴 𝐡 𝐢 𝐷 after reflection in the 𝑦 -axis.

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

Q7:

List the images of the labelled points under reflection in the 𝑦 -axis.

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

Q8:

What is the image of the point ( βˆ’ 8 , 1 0 ) reflected in the 𝑦 -axis?

  • A ( βˆ’ 8 , 1 0 )
  • B ( βˆ’ 8 , βˆ’ 1 0 )
  • C ( 8 , βˆ’ 1 0 )
  • D ( 8 , 1 0 )
  • E ( 1 0 , βˆ’ 8 )

Q9:

What is the image of the point ( βˆ’ 1 4 , 8 ) after a reflection in the π‘₯ -axis?

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

Q10:

Which pair of triangles represents a reflection in the π‘₯ -axis?

  • A 𝐡 and 𝐢
  • B 𝐴 and 𝐢
  • C 𝐴 and 𝐡

Q11:

Determine the image points of the rhombus 𝐴 𝐡 𝐢 𝐷 by reflection in the π‘₯ -axis.

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

Q12:

List the images of the points 𝐴 ( 5 , 4 ) , 𝐡 ( 8 , 6 ) , and 𝐢 ( 9 , βˆ’ 8 ) , after reflection in the 𝑦 -axis.

  • A 𝐴 β€² ( βˆ’ 5 , 4 ) , 𝐡 β€² ( 8 , βˆ’ 6 ) , 𝐢 β€² ( βˆ’ 9 , βˆ’ 8 )
  • B 𝐴 β€² ( 5 , βˆ’ 4 ) , 𝐡 β€² ( βˆ’ 8 , 6 ) , 𝐢 β€² ( βˆ’ 9 , βˆ’ 8 )
  • C 𝐴 β€² ( βˆ’ 5 , 4 ) , 𝐡 β€² ( βˆ’ 8 , 6 ) , 𝐢 β€² ( 9 , 8 )
  • D 𝐴 β€² ( βˆ’ 5 , 4 ) , 𝐡 β€² ( βˆ’ 8 , 6 ) , 𝐢 β€² ( βˆ’ 9 , βˆ’ 8 )
  • E 𝐴 β€² ( 5 , βˆ’ 4 ) , 𝐡 β€² ( 8 , βˆ’ 6 ) , 𝐢 β€² ( 9 , 8 )

Q13:

Farida and Nader are trying to find the coordinates of the image of after a reflection over the -axis. Farida’s answer was , while Nader’s answer was . Which of them is correct?

  • AFarida
  • BNader

Q14:

A line segment with a length of 6 is reflected in the 𝑦 -axis. What is the length of its image?

Q15:

An angle with a size of is reflected in the -axis. What is the size of its image?

  • A
  • B
  • C
  • D
  • E

Q16:

A point is transformed by a reflection in the line 𝑦 = βˆ’ π‘₯ . Which of the following functions represents this reflection?

  • A ( π‘₯ , 𝑦 ) β†’ ( π‘₯ , βˆ’ 𝑦 )
  • B ( π‘₯ , 𝑦 ) β†’ ( βˆ’ π‘₯ , βˆ’ 𝑦 )
  • C ( π‘₯ , 𝑦 ) β†’ ( βˆ’ 𝑦 , π‘₯ )
  • D ( π‘₯ , 𝑦 ) β†’ ( βˆ’ 𝑦 , βˆ’ π‘₯ )
  • E ( π‘₯ , 𝑦 ) β†’ ( 𝑦 , π‘₯ )

Q17:

𝐴 𝐡 has a length of 3. It is reflected in the π‘₯ -axis to 𝐴 β€² 𝐡 β€² . What is the length of 𝐴 β€² 𝐡 β€² ?

Q18:

In the figure, 𝐴 𝐡 has been reflected in the 𝑦 -axis. Is the length of the image resulting from this transformation greater than, less than, or the same as the length of 𝐴 𝐡 ?

  • Aless than
  • Bgreater than
  • Cthe same

Q19:

Three points 𝐴 , 𝐡 , and 𝐢 with coordinates (1, 3), (1, 2), and (4, 1), respectively, are reflected in the π‘₯ -axis to the points 𝐴  , 𝐡  , and 𝐢  .

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

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

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

Q20:

Two parallel lines are reflected in the 𝑦 -axis. Are the resulting two lines parallel to each other, or do they intersect?

  • AThey are parallel.
  • BThey intersect.

Q21:

What are the coordinates of the reflection of point 𝐢 ( βˆ’ 2 , 6 ) across the π‘₯ -axis?

  • A ( 2 , 6 )
  • B ( βˆ’ 2 , 6 )
  • C ( 2 , βˆ’ 6 )
  • D ( βˆ’ 2 , βˆ’ 6 )

Q22:

Two points 𝐴 and 𝐡 have coordinates (2, 4) and (4, 4) respectively. 𝐴 𝐡 is reflected in the 𝑦 -axis to 𝐴 𝐡   .

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

  • A 𝐴 β€² = ( βˆ’ 2 , βˆ’ 4 ) , 𝐡 β€² = ( βˆ’ 4 , βˆ’ 4 )
  • B 𝐴 β€² = ( 2 , βˆ’ 4 ) , 𝐡 β€² = ( 4 , βˆ’ 4 )
  • C 𝐴 β€² = ( βˆ’ 4 , 2 ) , 𝐡 β€² = ( βˆ’ 4 , 4 )
  • D 𝐴 β€² = ( βˆ’ 2 , 4 ) , 𝐡 β€² = ( βˆ’ 4 , 4 )
  • E 𝐴 β€² = ( 4 , βˆ’ 2 ) , 𝐡 β€² = ( 4 , βˆ’ 4 )

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

  • Aequal to
  • Bless than
  • Cgreater than

Q23:

What are the coordinates of the reflection of point 𝐼 ( 7 , 1 1 ) across both axes?

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

Q24:

Two intersecting lines are reflected in the π‘₯ -axis. Is it possible for the images of the two lines to be parallel?

  • Ano
  • Byes

Q25:

What are the coordinates of the reflection of point 𝐡 ( 2 , 8 ) across the 𝑦 -axis?

  • A ( 2 , βˆ’ 8 )
  • B ( 2 , 8 )
  • C ( βˆ’ 2 , βˆ’ 8 )
  • D ( βˆ’ 2 , 8 )

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