Worksheet: Reflections on the Coordinate Plane

In this worksheet, we will practice finding the images of points, lines, and shapes after their reflection in the x- or y-axis on the coordinate plane.

Q1:

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

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

Q2:

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

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

Q3:

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

  • A𝐴′(2,βˆ’4)
  • B𝐴′(4,2)
  • C𝐴′(βˆ’2,βˆ’4)
  • D𝐴′(βˆ’2,4)

Q4:

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

  • A𝐴′ is (1,βˆ’3), 𝐡′ is (5,βˆ’4)
  • B𝐴′ is (βˆ’1,3), 𝐡′ is (βˆ’5,4)
  • C𝐴′ is (βˆ’1,βˆ’3), 𝐡′ is (βˆ’5,βˆ’4)

Q5:

Find the images of 𝐴𝐡𝐢𝐷 after reflection in the 𝑦-axis.

  • A𝐴′(8,6),𝐡′(8,1),𝐢′(βˆ’2,1),𝐷′(βˆ’2,6)
  • B𝐴′(βˆ’8,6),𝐡′(βˆ’8,1),𝐢′(βˆ’2,1),𝐷′(βˆ’2,6)
  • C𝐴′(βˆ’8,βˆ’6),𝐡′(βˆ’8,βˆ’1),𝐢′(βˆ’2,βˆ’1),𝐷′(βˆ’2,βˆ’6)
  • D𝐴′(8,βˆ’6),𝐡′(8,βˆ’1),𝐢′(2,βˆ’1),𝐷′(2,βˆ’6)

Q6:

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

  • A𝐴′(βˆ’2,βˆ’5),𝐡′(0,βˆ’4),𝐢′(3,βˆ’3),𝐷′(4,1),𝐸′(βˆ’4,0)
  • B𝐴′(2,5),𝐡′(0,4),𝐢′(βˆ’3,3),𝐷′(βˆ’4,βˆ’1),𝐸′(4,0)
  • C𝐴′(βˆ’5,βˆ’2),𝐡′(βˆ’4,0),𝐢′(βˆ’3,3),𝐷′(1,4),𝐸′(0,βˆ’4)
  • D𝐴′(5,2),𝐡′(4,0),𝐢′(3,βˆ’3),𝐷′(βˆ’1,βˆ’4),𝐸′(0,4)

Q7:

What is the image of the point (βˆ’8,10) reflected in the 𝑦-axis?

  • A(10,βˆ’8)
  • B(8,10)
  • C(βˆ’8,βˆ’10)
  • D(βˆ’8,10)
  • E(8,βˆ’10)

Q8:

What is the image of the point (βˆ’14,8) after a reflection in the π‘₯-axis?

  • A(βˆ’14,βˆ’8)
  • B(8,βˆ’14)
  • C(14,βˆ’8)
  • D(βˆ’14,8)
  • E(14,8)

Q9:

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

  • A𝐡 and 𝐢
  • B𝐴 and 𝐡
  • C𝐴 and 𝐢

Q10:

Determine the image points of the rhombus𝐴𝐡𝐢𝐷 by reflection in the π‘₯-axis.

  • A𝐴(βˆ’6,6), 𝐡(βˆ’8,4), 𝐢(βˆ’6,2), 𝐷(βˆ’4,4)
  • B𝐴(6,6), 𝐡(8,4), 𝐢(βˆ’6,2), 𝐷(βˆ’4,4)
  • C𝐴(6,βˆ’6), 𝐡(8,βˆ’4), 𝐢(6,βˆ’2), 𝐷(4,βˆ’4)
  • D𝐴(βˆ’6,βˆ’6), 𝐡(βˆ’8,βˆ’4), 𝐢(βˆ’6,βˆ’2), 𝐷(βˆ’4,βˆ’4)
  • E𝐴(6,βˆ’6), 𝐡(8,βˆ’4), 𝐢(βˆ’6,βˆ’2), 𝐷(βˆ’4,βˆ’4)

Q11:

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

  • A𝐴′(βˆ’5,4), 𝐡′(βˆ’8,6), 𝐢′(βˆ’9,βˆ’8)
  • B𝐴′(5,βˆ’4), 𝐡′(8,βˆ’6), 𝐢′(9,8)
  • C𝐴′(βˆ’5,4), 𝐡′(8,βˆ’6), 𝐢′(βˆ’9,βˆ’8)
  • D𝐴′(βˆ’5,4), 𝐡′(βˆ’8,6), 𝐢′(9,8)
  • E𝐴′(5,βˆ’4), 𝐡′(βˆ’8,6), 𝐢′(βˆ’9,βˆ’8)

Q12:

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

  • AMason
  • BScarlett

Q13:

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

Q14:

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′, 𝐡′, and 𝐢′.

  • A𝐴′=(3,βˆ’1), 𝐡′=(2,βˆ’1), 𝐢′=(1,βˆ’4)
  • B𝐴′=(1,βˆ’3), 𝐡′=(1,βˆ’2), 𝐢′=(4,βˆ’1)
  • C𝐴′=(βˆ’3,1), 𝐡′=(βˆ’2,1), 𝐢′=(βˆ’1,4)
  • D𝐴′=(βˆ’1,βˆ’3), 𝐡′=(βˆ’1,βˆ’2), 𝐢′=(βˆ’4,βˆ’1)
  • E𝐴′=(βˆ’1,3), 𝐡′=(βˆ’1,2), 𝐢′=(βˆ’4,1)

Is the measure of angle 𝐴𝐡𝐢 less than, greater than, or equal to the measure of angle 𝐴′𝐡′𝐢′?

  • Agreater than
  • Bless than
  • Cequal to

Q15:

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

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

Q16:

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

Determine the coordinates of 𝐴′ and 𝐡′.

  • A𝐴′=(4,βˆ’2), 𝐡′=(4,βˆ’4)
  • B𝐴′=(βˆ’4,2), 𝐡′=(βˆ’4,4)
  • C𝐴′=(βˆ’2,βˆ’4), 𝐡′=(βˆ’4,βˆ’4)
  • D𝐴′=(βˆ’2,4), 𝐡′=(βˆ’4,4)
  • E𝐴′=(2,βˆ’4), 𝐡′=(4,βˆ’4)

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

  • Aless than
  • Bgreater than
  • Cequal to

Q17:

What are the coordinates of the reflection of point 𝐼(7,11) across both axes?

  • A(βˆ’7,βˆ’11)
  • B(7,βˆ’11)
  • C(7,11)
  • D(βˆ’7,11)

Q18:

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’2,8)
  • D(βˆ’2,βˆ’8)

Q19:

Determine the image points of the rectangle𝐴𝐡𝐢𝐷 after a reflection in the 𝑦-axis.

  • A𝐴′(8,4), 𝐡′(8,2), 𝐢′(βˆ’5,2), 𝐷′(βˆ’5,4)
  • B𝐴′(βˆ’8,4), 𝐡′(8,βˆ’2), 𝐢′(5,βˆ’2), 𝐷′(5,βˆ’4)
  • C𝐴′(βˆ’8,βˆ’4), 𝐡′(βˆ’8,βˆ’2), 𝐢′(βˆ’5,βˆ’2), 𝐷′(βˆ’5,βˆ’4)
  • D𝐴′(βˆ’8,4), 𝐡′(βˆ’8,2), 𝐢′(βˆ’5,2), 𝐷′(βˆ’5,4)
  • E𝐴′(8,βˆ’4), 𝐡′(8,βˆ’2), 𝐢′(5,βˆ’2), 𝐷′(5,βˆ’4)

Q20:

The points 𝐴(βˆ’8,2), 𝐡(βˆ’2,4), 𝐢(βˆ’3,βˆ’3), and 𝐷(βˆ’7,βˆ’3) are vertices of a quadrilateral. Determine the coordinates of point 𝐷 after a reflection in the 𝑦-axis.

  • A(7,3)
  • B(βˆ’7,3)
  • C(7,βˆ’3)
  • D(βˆ’3,βˆ’7)
  • E(βˆ’3,7)

Q21:

If ⃖⃗𝐴𝐡 is reflected in the π‘₯-axis, will its image be a point, a line segment, or a line?

  • Aa point
  • Ba line segment
  • Ca line

Q22:

List the images of the points 𝐴(βˆ’5,7), 𝐡(5,8), 𝐢(3,βˆ’5), and 𝐷(βˆ’7,βˆ’3), after reflection in the π‘₯-axis.

  • A𝐴′(5,7), 𝐡′(βˆ’5,8), 𝐢′(βˆ’3,βˆ’5), 𝐷′(7,βˆ’3)
  • B𝐴′(βˆ’5,βˆ’7), 𝐡′(5,βˆ’8), 𝐢′(3,5), 𝐷′(βˆ’7,3)
  • C𝐴′(βˆ’5,βˆ’7), 𝐡′(5,βˆ’8), 𝐢′(βˆ’3,βˆ’5), 𝐷′(7,βˆ’3)
  • D𝐴′(βˆ’5,βˆ’7), 𝐡′(βˆ’5,8), 𝐢′(βˆ’3,βˆ’5), 𝐷′(βˆ’7,3)
  • E𝐴′(5,7), 𝐡′(βˆ’5,8), 𝐢′(3,5), 𝐷′(βˆ’7,3)

Q23:

What is the image of point (5,5) under point reflection in the origin?

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

Q24:

Reflect triangle 𝐴𝐡𝐢 in the π‘₯-axis, and state the coordinates of the image.

  • A(βˆ’2,0),(1,βˆ’2),(1,3)
  • B(0,2),(βˆ’1,1),(3,1)
  • C(2,0),(1,2),(1,βˆ’3)
  • D(0,βˆ’2),(βˆ’2,1),(1,3)
  • E(2,0),(βˆ’1,2),(βˆ’1,3)

Q25:

Reflect the given triangle in the π‘₯-axis. Which of the following sets of coordinates will be the vertices of the image?

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

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