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Worksheet: Reflections

Q1:

Given that vertices 𝐽 ( βˆ’ 8 , 8 ) , 𝐾 ( 3 , βˆ’ 9 ) , and 𝐿 ( βˆ’ 3 , 5 ) form a triangle, without graphing, determine their coordinates after a reflection over the π‘₯ -axis first and then over the 𝑦 -axis.

  • A 𝐽 β€² β€² ( 8 , βˆ’ 8 ) , 𝐾 β€² β€² ( 3 , 9 ) , 𝐿 β€² β€² ( 3 , βˆ’ 5 )
  • B 𝐽 β€² β€² ( 8 , βˆ’ 8 ) , 𝐾 β€² β€² ( βˆ’ 3 , 9 ) , 𝐿 β€² β€² ( βˆ’ 3 , βˆ’ 5 )
  • C 𝐽 β€² β€² ( 8 , 8 ) , 𝐾 β€² β€² ( βˆ’ 3 , βˆ’ 9 ) , 𝐿 β€² β€² ( 3 , 5 )
  • D 𝐽 β€² β€² ( 8 , βˆ’ 8 ) , 𝐾 β€² β€² ( βˆ’ 3 , 9 ) , 𝐿 β€² β€² ( 3 , βˆ’ 5 )
  • E 𝐽 β€² β€² ( βˆ’ 8 , βˆ’ 8 ) , 𝐾 β€² β€² ( 3 , 9 ) , 𝐿 β€² β€² ( βˆ’ 3 , βˆ’ 5 )

Q2:

The given figure shows triangle 𝐴 β€² 𝐡 β€² 𝐢 β€² after a reflection in the π‘₯ -axis. Determine the original coordinates of point 𝐢 .

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

Q3:

The given figure shows triangle 𝐴 β€² 𝐡 β€² 𝐢 β€² after a reflection in the 𝑦 -axis. Determine the original coordinates of point 𝐴 .

  • A ( 3 , βˆ’ 5 )
  • B ( 5 , 3 )
  • C ( βˆ’ 3 , βˆ’ 5 )
  • D ( 3 , 5 )
  • E ( 5 , βˆ’ 3 )

Q4:

is a rectangle, and the point is the reflection of in . If , what is ?

  • A
  • B
  • C
  • D

Q5:

Suppose that π‘Ž β‰  0 . What is the relation between lines 𝑦 = π‘Ž π‘₯ + 𝑏 and 𝑦 = ο€Ό 1 π‘Ž  π‘₯ + 𝑏 ?

  • A They are parallel.
  • B They are perpendicular.
  • C They are mirror images in 𝑦 = 𝑏 .
  • D They are mirror images in 𝑦 = π‘₯ + 𝑏 .
  • EIt cannot be determined.

Q6:

What are the coordinates of the reflection, in the line π‘₯ = 2 , of the point ( βˆ’ 5 , 9 ) ?

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

Q7:

The graph of a function 𝑓 ( π‘₯ ) is transformed by mapping each point on the function ( π‘₯ , 𝑦 ) to the point ( 𝑦 , π‘₯ ) . This image is a reflection of 𝑓 ( π‘₯ ) in .

  • Athe π‘₯ -axis
  • Bthe line 𝑦 = βˆ’ π‘₯
  • Cthe 𝑦 -axis
  • Dthe line 𝑦 = π‘₯
  • Ethe line π‘₯ 𝑦 = 1

Q8:

A rectangle 𝐴 𝐡 𝐢 𝐷 is reflected in βƒ–      βƒ— 𝐴 𝐷 and a larger rectangle is formed by joining 𝐴 𝐡 𝐢 𝐷 and its reflection. Given that 𝐴 𝐡 = 8 4 c m and 𝐢 𝐡 = 4 7 c m , find the perimeter of the larger rectangle.

Q9:

The point ( 3 , 5 ) is reflected to the point ( 3 , 7 ) . Was the line of reflection horizontal or vertical?

  • Ahorizontal
  • Bvertical

Q10:

Points and have coordinates and respectively. Given that is the image of after a reflection in the -axis, find the perimeter of .

Q11:

In the figure, 𝐴 𝐡 𝐢 𝐷 is a square with center 𝐿 . Find the image of the square 𝐴 𝐸 𝐿 𝐺 after a reflection in βƒ–      βƒ— 𝐺 𝐻 .

  • A 𝐴 𝐺 𝐿 𝐸
  • B 𝐡 𝐸 𝐿 𝐻
  • C 𝐢 𝐻 𝐿 𝐹
  • D 𝐷 𝐹 𝐿 𝐺

Q12:

Given that β–³ 𝐴 β€² 𝐡 β€² 𝐢 β€² is the image of β–³ 𝐴 𝐡 𝐢 after a reflection in the line 𝑀 , give the coordinates of 𝐴 β€² , 𝐡 β€² and 𝐢 β€² .

  • A 𝐴 β€² ( 6 , 2 ) i s , 𝐡 β€² ( 8 , 0 ) i s , 𝐢 β€² ( 1 2 , 3 ) i s
  • B 𝐴 β€² ( 6 , 2 ) i s , 𝐡 β€² ( 4 , 0 ) i s , 𝐢 β€² ( 0 , 3 ) i s
  • C 𝐴 β€² ( 6 , 6 ) i s , 𝐡 β€² ( 4 , 8 ) i s , 𝐢 β€² ( 0 , 5 ) i s

Q13:

Points ( 2 , 4 ) , ( 6 , 0 ) , ( 8 , 3 ) , ( 8 , 7 ) , ( 6 , 8 ) , and ( 3 , 7 ) are the vertices of a polygon. List their images after a reflection in the vertical line through ( 1 1 , 0 ) .

  • A ( βˆ’ 9 , 4 ) , ( βˆ’ 5 , 0 ) , ( βˆ’ 3 , 3 ) , ( βˆ’ 3 , 7 ) , ( βˆ’ 5 , 8 ) , ( βˆ’ 8 , 7 )
  • B ( 1 3 , 4 ) , ( 1 7 , 0 ) , ( 1 9 , 3 ) , ( 1 9 , 7 ) , ( 1 7 , 8 ) , ( 1 4 , 7 )
  • C ( 2 4 , 4 ) , ( 2 8 , 0 ) , ( 3 0 , 3 ) , ( 3 0 , 7 ) , ( 2 8 , 8 ) , ( 2 5 , 7 )
  • D ( 2 0 , 4 ) , ( 1 6 , 0 ) , ( 1 4 , 3 ) , ( 1 4 , 7 ) , ( 1 6 , 8 ) , ( 1 9 , 7 )
  • E ( 2 , 1 8 ) , ( 6 , 2 2 ) , ( 8 , 1 9 ) , ( 8 , 1 5 ) , ( 6 , 1 4 ) , ( 3 , 1 5 )

Q14:

What is the image of the point ( 9 , 8 ) under reflection in the straight line 𝑦 = π‘₯ ?

  • A ( βˆ’ 9 , βˆ’ 8 )
  • B ( 9 , βˆ’ 8 )
  • C ο€Ό 1 9 , 1 8 
  • D ( 8 , 9 )
  • E ο€Ό 9 , 1 8 

Q15:

The image of the point 𝐴 ( 5 , βˆ’ 3 ) is 𝐴 β€² ( 3 , βˆ’ 5 ) when reflected in a line. Find the equation of the line of reflection.

  • A 𝑦 = βˆ’ π‘₯ βˆ’ 8
  • B 𝑦 = π‘₯
  • C 𝑦 = π‘₯ βˆ’ 8
  • D 𝑦 = βˆ’ π‘₯

Q16:

Across which line has β–³ 𝐡 𝐸 𝐹 been reflected to get β–³ 𝐴 𝐸 𝐹 ?

  • A βƒ–     βƒ— 𝐹 𝐡
  • B βƒ–     βƒ— 𝐹 𝐷
  • C βƒ–     βƒ— 𝐸 𝐹

Q17:

If 𝐢 𝐷 is the image of 𝐡 𝐴 by reflection in the point 𝑀 , 𝐴 𝐡 = ( 2 π‘₯ + 4 ) c m , 𝐢 𝐷 = ( π‘₯ + 8 ) c m , π‘š ∠ 𝐡 𝐴 𝐷 = ( 1 1 𝑦 ) ∘ and π‘š ∠ 𝐴 𝐷 𝐢 = 4 4 ∘ , find the length of 𝐢 𝐷 and the value of 𝑦 .

  • A 32 cm, 4
  • B 6 cm, 11
  • C 12 cm, 15
  • D 12 cm, 4

Q18:

Find the image of β–³ 𝐴 𝐺 𝐿 by reflection in βƒ–     βƒ— 𝐴 𝐢 .

  • A β–³ 𝐷 𝐺 𝐿
  • B β–³ 𝐡 𝐻 𝐿
  • C β–³ 𝐢 𝐹 𝐿
  • D β–³ 𝐴 𝐸 𝐿

Q19:

What type of transformation is the following?

  • Atranslation
  • Brotation
  • Creflection