Worksheets · Geometry

Reflections worksheet for Geometry

Reflecting over the x-axis flips the sign of y, over the y-axis flips the sign of x, and over the line y = x swaps them. Over y = -x they swap and both change sign, and over a line like x = 5 the point lands the same distance away on the other side.

Also taught in Pre-Algebra, at its own level and with its own examples.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Reflections

Date Period

Reflect each point or figure.

  1. Reflect the figure on the grid

    Reflect the triangle across the y-axis.−10−10−5−5551010ABC
  2. Draw the image of the triangle after a reflection in the x-axis.−10−10−5551010ABC−5
  3. Reflect over the line y=x.−10−10−5−551010ABC5
  4. Draw the image of the triangle after a reflection in the y-axis.−10−10−5−5551010ABC
  5. Reflect the triangle across the line y=x.−10−10−5551010ABC−5
  6. Reflect over the x-axis.−10−10−5−5551010ABC
  7. Reflect over the y-axis.−10−10−5−5551010ABC
  8. Draw the image of the triangle after a reflection in the line y=x.−10−10−5−551010ABC5
  9. Reflect over the x-axis.−10−10−5−5551010ABC
  10. Reflect the triangle across the x-axis.−10−10−5−5551010ABC

  1. Find the image after reflecting over the given line

    The line y=3 is a mirror. Find the mirror image of (−6,5).
  2. The point (−6,−5) is reflected across x=4. Give the coordinates of the image.
  3. Where do the vertices of triangle A(6,1), B(1,−1), C(2,1) land when they are reflected in x=−5?
  4. Find the image of (2,0) after a reflection in the line y=−x.
  5. Reflect (−2,−5) over the line x=2.
  6. The line y=−2 is a mirror. Find the mirror image of triangle A(−4,−1), B(7,3), C(1,5).
  7. Reflect (−1,7) over the line y=−x.
  8. The point (−7,5) is reflected across x=−2. Give the coordinates of the image.
  9. Where do the vertices of triangle A(−1,7), B(0,−6), C(−3,3) land when they are reflected in y=−1?
  10. Find the image of (7,6) after a reflection in the line y=4.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

ReflectionsAnswer keyVersion 1

Date Period

Reflect each point or figure.

  1. Reflect the figure on the grid

    Reflect the triangle across the y-axis.−10−10−5−5551010ABCA′B′C′A′(6,4), B′(2,4), C′(6,1)
  2. Draw the image of the triangle after a reflection in the x-axis.−10−10−551010ABCA′B′C′−55A′(−1,9), B′(4,9), C′(−2,4)
  3. Reflect over the line y=x.−10−10−5−51010ABCA′B′C′55A′(−1,4), B′(−6,4), C′(−1,7)
  4. Draw the image of the triangle after a reflection in the y-axis.−10−10−5−5551010ABCA′B′C′A′(−2,4), B′(−2,7), C′(−6,5)
  5. Reflect the triangle across the line y=x.−10−10551010ABCA′B′C′−5−5A′(−2,−5), B′(2,−5), C′(2,−9)
  6. Reflect over the x-axis.−10−10−5−5551010ABCA′B′C′A′(−8,−6), B′(−3,−8), C′(−4,−5)
  7. Reflect over the y-axis.−10−10−5−5551010ABCA′B′C′A′(−8,5), B′(−6,8), C′(−4,5)
  8. Draw the image of the triangle after a reflection in the line y=x.−10−10−5−51010ABCA′B′C′55A′(−1,3), B′(2,4), C′(−1,7)
  9. Reflect over the x-axis.−10−10−5−5551010ABCA′B′C′A′(−2,−3), B′(−3,−7), C′(−7,−5)
  10. Reflect the triangle across the x-axis.−10−10−5−5551010ABCA′B′C′A′(−5,5), B′(−5,9), C′(−8,7)

  1. Find the image after reflecting over the given line

    The line y=3 is a mirror. Find the mirror image of (−6,5).(−6,1)
  2. The point (−6,−5) is reflected across x=4. Give the coordinates of the image.(14,−5)
  3. Where do the vertices of triangle A(6,1), B(1,−1), C(2,1) land when they are reflected in x=−5?A′(−16,1), B′(−11,−1), C′(−12,1)
  4. Find the image of (2,0) after a reflection in the line y=−x.(0,−2)
  5. Reflect (−2,−5) over the line x=2.(6,−5)
  6. The line y=−2 is a mirror. Find the mirror image of triangle A(−4,−1), B(7,3), C(1,5).A′(−4,−3), B′(7,−7), C′(1,−9)
  7. Reflect (−1,7) over the line y=−x.(−7,1)
  8. The point (−7,5) is reflected across x=−2. Give the coordinates of the image.(3,5)
  9. Where do the vertices of triangle A(−1,7), B(0,−6), C(−3,3) land when they are reflected in y=−1?A′(−1,−9), B′(0,4), C′(−3,−5)
  10. Find the image of (7,6) after a reflection in the line y=4.(7,2)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Reflect (3,−5) over the y-axis

  1. The y-axis flips the x.
  2. So 3 becomes -3.
  3. The y is untouched.

The answer is (−3,−5).

Where students go wrong

Flipping the coordinate that matches the axis name. Reflecting over the x-axis changes the y, not the x, because the x-axis is the mirror and points move perpendicular to it.

Also called reflecting points, reflection over the x-axis or reflection over y = x.

What you can put on this worksheet

On a grid, with the image drawn
Draw the image of the triangle after a reflection in the y-axis. → A′(5,3), B′(9,3), C′(7,6)
Reflecting over an axis or y = x
Reflect (3,1) over the y-axis. → (−3,1)
Over x = a, y = b and y = -x
The point (−6,0) is reflected across y=4. Give the coordinates of the image. → (−6,8)
Over y = -x, x = a or y = b, on a grid
Reflect over the line x=1. → (−2,3), (−2,7), (−5,6)
A figure given as a list of vertices
Reflect the points across the y-axis:
P(0,1), T(−4,7), B(−2,5). List the image of each point. → P′(0,1), T′(4,7), B′(2,5)
Name the reflection and write its rule
Name the transformation and write its rule. → Reflection across the line y=−x: (x,y)→(−y,−x)

Questions about these worksheets

Yes. Every reflections sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the reflections questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 6: on a grid, with the image drawn, reflecting over an axis or y = x, over x = a, y = b and y = -x, over y = -x, x = a or y = b, on a grid, a figure given as a list of vertices and name the reflection and write its rule. Tick as many as you want and set how many of each, or let it spread them evenly.

Flipping the coordinate that matches the axis name. Reflecting over the x-axis changes the y, not the x, because the x-axis is the mirror and points move perpendicular to it.