Worksheet: Reflections

In this worksheet, we will practice identifying an image, an object, and a mirror line and applying this knowledge in various situations.

Q1:

A rectangle 𝐴 𝐵 𝐶 𝐷 is reflected in 𝐴 𝐷 and a larger rectangle is formed by joining 𝐴 𝐵 𝐶 𝐷 and its reflection. Given that 𝐴 𝐵 = 8 4 c m and 𝐶 𝐵 = 4 7 c m , find the perimeter of the larger rectangle.

Q2:

The points 𝐽 ( 8 , 8 ) , 𝐾 ( 3 , 9 ) , and 𝐿 ( 3 , 5 ) form a triangle. Without graphing, determine their coordinates after a reflection in the 𝑥 -axis, followed by a reflection in the 𝑦 -axis.

  • A 𝐽 ( 8 , 8 ) , 𝐾 ( 3 , 9 ) , 𝐿 ( 3 , 5 )
  • B 𝐽 ( 8 , 8 ) , 𝐾 ( 3 , 9 ) , 𝐿 ( 3 , 5 )
  • C 𝐽 ( 8 , 8 ) , 𝐾 ( 3 , 9 ) , 𝐿 ( 3 , 5 )
  • D 𝐽 ( 8 , 8 ) , 𝐾 ( 3 , 9 ) , 𝐿 ( 3 , 5 )
  • E 𝐽 ( 8 , 8 ) , 𝐾 ( 3 , 9 ) , 𝐿 ( 3 , 5 )

Q3:

The given figure shows triangle 𝐴 𝐵 𝐶 after a reflection in the 𝑦 -axis. Determine the original coordinates of point 𝐴 .

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

Q4:

Given that 𝐴 𝐵 𝐶 is the image of 𝐴 𝐵 𝐶 after a reflection in the line 𝑀 , give the coordinates of 𝐴 , 𝐵 and 𝐶 .

  • A 𝐴 is ( 6 , 2 ) , 𝐵 is ( 8 , 0 ) , 𝐶 is ( 1 2 , 3 )
  • B 𝐴 is ( 6 , 2 ) , 𝐵 is ( 4 , 0 ) , 𝐶 is ( 0 , 3 )
  • C 𝐴 is ( 6 , 6 ) , 𝐵 is ( 4 , 8 ) , 𝐶 is ( 0 , 5 )

Q5:

Points 𝐴 and 𝐵 have coordinates ( 7 , 8 ) and ( 7 , 4 ) respectively. Given that 𝐷 𝐶 is the image of 𝐴 𝐵 after a reflection in the 𝑦 -axis, find the perimeter of 𝐴 𝐵 𝐶 𝐷 .

Q6:

𝐴 𝐵 𝐶 𝐷 is a rectangle, and the point 𝐶 is the reflection of 𝐶 in 𝐴 𝐵 . If 𝑚 𝐶 𝐴 𝐵 = 7 1 , what is 𝑚 𝐶 𝐴 𝐶 ?

Q7:

What are the coordinates of the reflection, in the line 𝑥 = 2 , of the point ( 5 , 9 ) ?

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

Q8:

In the figure, 𝐴 𝐵 𝐶 𝐷 is a square with centre 𝐿 . Find the image of the square 𝐴 𝐸 𝐿 𝐺 after a reflection in 𝐺 𝐻 .

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

Q9:

What type of transformation is the following?

  • Atranslation
  • Brotation
  • Creflection

Q10:

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

  • Ahorizontal
  • Bvertical

Q11:

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 ( 9 , 4 ) , ( 5 , 0 ) , ( 3 , 3 ) , ( 3 , 7 ) , ( 5 , 8 ) , ( 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 )

Q12:

What is the image of the point ( 9 , 8 ) under reflection in the straight line 𝑦 = 𝑥 ?

  • A ( 9 , 8 )
  • B ( 9 , 8 )
  • C 1 9 , 1 8
  • D ( 8 , 9 )
  • E 9 , 1 8

Q13:

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

  • A 𝑦 = 𝑥 8
  • B 𝑦 = 𝑥
  • C 𝑦 = 𝑥 8
  • D 𝑦 = 𝑥
  • E 𝑦 = 𝑥 8

Q14:

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

  • Athe 𝑥 -axis
  • Bthe line 𝑦 = 𝑥
  • Cthe 𝑦 -axis
  • Dthe line 𝑦 = 𝑥
  • Ethe line 𝑥 𝑦 = 1

Q15:

Across which line has 𝐵 𝐸 𝐹 been reflected to get 𝐴 𝐸 𝐹 ?

  • A 𝐹 𝐵
  • B 𝐹 𝐷
  • C 𝐸 𝐹

Q16:

If 𝐶 𝐷 is the image of 𝐵 𝐴 by reflection in the point 𝑀 , 𝐴 𝐵 = ( 2 𝑥 + 4 ) c m , 𝐶 𝐷 = ( 𝑥 + 8 ) c m , 𝑚 𝐵 𝐴 𝐷 = ( 1 1 𝑦 ) and 𝑚 𝐴 𝐷 𝐶 = 4 4 , find the length of 𝐶 𝐷 and the value of 𝑦 .

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

Q17:

Find the image of 𝐴 𝐺 𝐿 by reflection in 𝐴 𝐶 .

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

Q18:

Suppose that 𝑎 0 . What is the relation between lines 𝑦 = 𝑎 𝑥 + 𝑏 and 𝑦 = 1 𝑎 𝑥 + 𝑏 ?

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

Q19:

The given figure shows triangle 𝐴 𝐵 𝐶 after a reflection in the 𝑦 -axis. Determine the original coordinates of point 𝐴 .

  • A ( 7 , 2 )
  • B ( 2 , 7 )
  • C ( 7 , 2 )
  • D ( 7 , 2 )
  • E ( 2 , 7 )

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