Worksheet: Reflections

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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 ( 𝑥 , 𝑦 ) is reflected in the 𝑦 -axis, determine the coordinates of the image.

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

Q2:

If a point with coordinates ( 𝑥 , 𝑦 ) is reflected in the 𝑥 -axis, determine the coordinates of the image.

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

Q3:

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

  • A 𝐴 ′ ( − 2 , 4 )
  • B 𝐴 ′ ( 4 , 2 )
  • C 𝐴 ′ ( − 2 , − 4 )
  • D 𝐴 ′ ( 2 , − 4 )

Q4:

Given that 𝐴 ′ 𝐵 ′ is the image of 𝐴 𝐵 by reflection in the 𝑦 -axis, find the coordinates of the points 𝐴 ′ and 𝐵 ′ .

  • A 𝐴 ′ is ( − 1 , 3 ) , 𝐵 ′ is ( − 5 , 4 )
  • B 𝐴 ′ is ( 1 , − 3 ) , 𝐵 ′ is ( 5 , − 4 )
  • C 𝐴 ′ is ( − 1 , − 3 ) , 𝐵 ′ is ( − 5 , − 4 )

Q5:

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

  • A 𝐴 and 𝐶
  • B 𝐵 and 𝐶
  • C 𝐴 and 𝐵

Q6:

Find the images of 𝐴 𝐵 𝐶 𝐷 after reflection in the 𝑦 -axis.

  • A 𝐴 ′ ( 8 , − 6 ) , 𝐵 ′ ( 8 , − 1 ) , 𝐶 ′ ( 2 , − 1 ) , 𝐷 ′ ( 2 , − 6 )
  • B 𝐴 ′ ( 8 , 6 ) , 𝐵 ′ ( 8 , 1 ) , 𝐶 ′ ( − 2 , 1 ) , 𝐷 ′ ( − 2 , 6 )
  • C 𝐴 ′ ( − 8 , 6 ) , 𝐵 ′ ( − 8 , 1 ) , 𝐶 ′ ( − 2 , 1 ) , 𝐷 ′ ( − 2 , 6 )
  • D 𝐴 ′ ( − 8 , − 6 ) , 𝐵 ′ ( − 8 , − 1 ) , 𝐶 ′ ( − 2 , − 1 ) , 𝐷 ′ ( − 2 , − 6 )

Q7:

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

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

Q8:

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

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

Q9:

What is the image of the point ( − 1 4 , 8 ) after a reflection in the 𝑥 -axis?

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

Q10:

Which pair of triangles represents a reflection in the 𝑥 -axis?

  • A 𝐵 and 𝐶
  • B 𝐴 and 𝐵
  • C 𝐴 and 𝐶

Q11:

Determine the image points of the rhombus 𝐴 𝐵 𝐶 𝐷 by reflection in the 𝑥 -axis.

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

Q12:

List the images of the points 𝐴 ( 5 , 4 ) , 𝐵 ( 8 , 6 ) , and 𝐶 ( 9 , − 8 ) , after reflection in the 𝑦 -axis.

  • A 𝐴 ′ ( − 5 , 4 ) , 𝐵 ′ ( − 8 , 6 ) , 𝐶 ′ ( − 9 , − 8 )
  • B 𝐴 ′ ( − 5 , 4 ) , 𝐵 ′ ( 8 , − 6 ) , 𝐶 ′ ( − 9 , − 8 )
  • C 𝐴 ′ ( − 5 , 4 ) , 𝐵 ′ ( − 8 , 6 ) , 𝐶 ′ ( 9 , 8 )
  • D 𝐴 ′ ( 5 , − 4 ) , 𝐵 ′ ( − 8 , 6 ) , 𝐶 ′ ( − 9 , − 8 )
  • E 𝐴 ′ ( 5 , − 4 ) , 𝐵 ′ ( 8 , − 6 ) , 𝐶 ′ ( 9 , 8 )

Q13:

Scarlett and Mason are trying to find the coordinates of the image of ( 4 , 9 ) after a reflection over the 𝑥 -axis. Scarlett’s answer was ( 4 , − 9 ) , while Mason’s answer was ( − 4 , 9 ) . Which of them is correct?

  • AMason
  • BScarlett

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 measure of 2 2 ∘ is reflected in the 𝑥 -axis. What is the measure of its image?

Q16:

A point is transformed by a reflection in the line 𝑦 = − 𝑥 . Which of the following functions represents this reflection?

  • A ( 𝑥 , 𝑦 ) → ( 𝑦 , 𝑥 )
  • B ( 𝑥 , 𝑦 ) → ( − 𝑦 , 𝑥 )
  • C ( 𝑥 , 𝑦 ) → ( − 𝑥 , − 𝑦 )
  • D ( 𝑥 , 𝑦 ) → ( − 𝑦 , − 𝑥 )
  • E ( 𝑥 , 𝑦 ) → ( 𝑥 , − 𝑦 )

Q17:

𝐴 𝐵 has a length of 3. It is reflected in the 𝑥 -axis to 𝐴 ′ 𝐵 ′ . What is the length of 𝐴 ′ 𝐵 ′ ?

Q18:

In the figure, 𝐴 𝐵 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 𝐵 ?

  • Athe same
  • Bgreater than
  • Cless than

Q19:

Three points 𝐴 , 𝐵 , and 𝐶 with coordinates (1, 3), (1, 2), and (4, 1), respectively, are reflected in the 𝑥 -axis to the points 𝐴 , 𝐵 , and 𝐶 .

Determine the coordinates of 𝐴 ′ , 𝐵 ′ , and 𝐶 ′ .

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

Is the measure of angle 𝐴 𝐵 𝐶 less than, greater than, or equal to the measure of angle 𝐴 ′ 𝐵 ′ 𝐶 ′ ?

  • 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 𝐶 ( − 2 , 6 ) across the 𝑥 -axis?

  • A ( 2 , − 6 )
  • B ( − 2 , 6 )
  • C ( 2 , 6 )
  • D ( − 2 , − 6 )

Q22:

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

Determine the coordinates of 𝐴 ′ and 𝐵 ′ .

  • A 𝐴 ′ = ( − 2 , − 4 ) , 𝐵 ′ = ( − 4 , − 4 )
  • B 𝐴 ′ = ( 2 , − 4 ) , 𝐵 ′ = ( 4 , − 4 )
  • C 𝐴 ′ = ( 4 , − 2 ) , 𝐵 ′ = ( 4 , − 4 )
  • D 𝐴 ′ = ( − 2 , 4 ) , 𝐵 ′ = ( − 4 , 4 )
  • E 𝐴 ′ = ( − 4 , 2 ) , 𝐵 ′ = ( − 4 , 4 )

Is the length of 𝐴 𝐵 greater than, less than, or equal to the length of 𝐴 ′ 𝐵 ′ ?

  • Aequal to
  • Bless than
  • Cgreater than

Q23:

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

  • A ( 7 , − 1 1 )
  • B ( − 7 , − 1 1 )
  • C ( − 7 , 1 1 )
  • D ( 7 , 1 1 )

Q24:

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

  • Ayes
  • Bno

Q25:

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

  • A ( 2 , 8 )
  • B ( − 2 , 8 )
  • C ( − 2 , − 8 )
  • D ( 2 , − 8 )

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