Worksheet: Reflections on the Coordinate Plane

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

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

Q2:

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

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

Q3:

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

  • A𝐴′(2,−4)
  • B𝐴′(4,2)
  • C𝐴′(−2,−4)
  • D𝐴′(−2,4)

Q4:

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

  • A𝐴′ is (1,−3), 𝐵′ is (5,−4)
  • B𝐴′ is (−1,3), 𝐵′ is (−5,4)
  • C𝐴′ is (−1,−3), 𝐵′ is (−5,−4)

Q5:

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

  • A𝐴′(8,6),𝐵′(8,1),𝐶′(−2,1),𝐷′(−2,6)
  • B𝐴′(−8,6),𝐵′(−8,1),𝐶′(−2,1),𝐷′(−2,6)
  • C𝐴′(−8,−6),𝐵′(−8,−1),𝐶′(−2,−1),𝐷′(−2,−6)
  • D𝐴′(8,−6),𝐵′(8,−1),𝐶′(2,−1),𝐷′(2,−6)

Q6:

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

  • A𝐴′(−2,−5),𝐵′(0,−4),𝐶′(3,−3),𝐷′(4,1),𝐸′(−4,0)
  • B𝐴′(2,5),𝐵′(0,4),𝐶′(−3,3),𝐷′(−4,−1),𝐸′(4,0)
  • C𝐴′(−5,−2),𝐵′(−4,0),𝐶′(−3,3),𝐷′(1,4),𝐸′(0,−4)
  • D𝐴′(5,2),𝐵′(4,0),𝐶′(3,−3),𝐷′(−1,−4),𝐸′(0,4)

Q7:

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

  • A(10,−8)
  • B(8,10)
  • C(−8,−10)
  • D(−8,10)
  • E(8,−10)

Q8:

What is the image of the point (−14,8) after a reflection in the 𝑥-axis?

  • A(−14,−8)
  • B(8,−14)
  • C(14,−8)
  • D(−14,8)
  • E(14,8)

Q9:

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

  • A𝐵 and 𝐶
  • B𝐴 and 𝐵
  • C𝐴 and 𝐶

Q10:

Determine the image points of the rhombus𝐴𝐵𝐶𝐷 by reflection in the 𝑥-axis.

  • A𝐴(−6,6), 𝐵(−8,4), 𝐶(−6,2), 𝐷(−4,4)
  • B𝐴(6,6), 𝐵(8,4), 𝐶(−6,2), 𝐷(−4,4)
  • C𝐴(6,−6), 𝐵(8,−4), 𝐶(6,−2), 𝐷(4,−4)
  • D𝐴(−6,−6), 𝐵(−8,−4), 𝐶(−6,−2), 𝐷(−4,−4)
  • E𝐴(6,−6), 𝐵(8,−4), 𝐶(−6,−2), 𝐷(−4,−4)

Q11:

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

  • A𝐴′(−5,4), 𝐵′(−8,6), 𝐶′(−9,−8)
  • B𝐴′(5,−4), 𝐵′(8,−6), 𝐶′(9,8)
  • C𝐴′(−5,4), 𝐵′(8,−6), 𝐶′(−9,−8)
  • D𝐴′(−5,4), 𝐵′(−8,6), 𝐶′(9,8)
  • E𝐴′(5,−4), 𝐵′(−8,6), 𝐶′(−9,−8)

Q12:

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

Q13:

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

Q14:

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′.

  • A𝐴′=(3,−1), 𝐵′=(2,−1), 𝐶′=(1,−4)
  • B𝐴′=(1,−3), 𝐵′=(1,−2), 𝐶′=(4,−1)
  • C𝐴′=(−3,1), 𝐵′=(−2,1), 𝐶′=(−1,4)
  • D𝐴′=(−1,−3), 𝐵′=(−1,−2), 𝐶′=(−4,−1)
  • E𝐴′=(−1,3), 𝐵′=(−1,2), 𝐶′=(−4,1)

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

  • Agreater than
  • Bless than
  • Cequal to

Q15:

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)

Q16:

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

Determine the coordinates of 𝐴′ and 𝐵′.

  • A𝐴′=(4,−2), 𝐵′=(4,−4)
  • B𝐴′=(−4,2), 𝐵′=(−4,4)
  • C𝐴′=(−2,−4), 𝐵′=(−4,−4)
  • D𝐴′=(−2,4), 𝐵′=(−4,4)
  • E𝐴′=(2,−4), 𝐵′=(4,−4)

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

  • Aless than
  • Bgreater than
  • Cequal to

Q17:

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

  • A(−7,−11)
  • B(7,−11)
  • C(7,11)
  • D(−7,11)

Q18:

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)

Q19:

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

  • A𝐴′(8,4), 𝐵′(8,2), 𝐶′(−5,2), 𝐷′(−5,4)
  • B𝐴′(−8,4), 𝐵′(8,−2), 𝐶′(5,−2), 𝐷′(5,−4)
  • C𝐴′(−8,−4), 𝐵′(−8,−2), 𝐶′(−5,−2), 𝐷′(−5,−4)
  • D𝐴′(−8,4), 𝐵′(−8,2), 𝐶′(−5,2), 𝐷′(−5,4)
  • E𝐴′(8,−4), 𝐵′(8,−2), 𝐶′(5,−2), 𝐷′(5,−4)

Q20:

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

  • A(7,3)
  • B(−7,3)
  • C(7,−3)
  • D(−3,−7)
  • E(−3,7)

Q21:

If ⃖⃗𝐴𝐵 is reflected in the 𝑥-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(−5,7), 𝐵(5,8), 𝐶(3,−5), and 𝐷(−7,−3), after reflection in the 𝑥-axis.

  • A𝐴′(5,7), 𝐵′(−5,8), 𝐶′(−3,−5), 𝐷′(7,−3)
  • B𝐴′(−5,−7), 𝐵′(5,−8), 𝐶′(3,5), 𝐷′(−7,3)
  • C𝐴′(−5,−7), 𝐵′(5,−8), 𝐶′(−3,−5), 𝐷′(7,−3)
  • D𝐴′(−5,−7), 𝐵′(−5,8), 𝐶′(−3,−5), 𝐷′(−7,3)
  • E𝐴′(5,7), 𝐵′(−5,8), 𝐶′(3,5), 𝐷′(−7,3)

Q23:

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

  • A(5,5)
  • B(−5,−5)
  • C(−5,5)
  • D(5,−5)

Q24:

Reflect triangle 𝐴𝐵𝐶 in the 𝑥-axis, and state the coordinates of the image.

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

Q25:

Reflect the given triangle in the 𝑥-axis. Which of the following sets of coordinates will be the vertices of the image?

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

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