8th Grade Translations, Reflections and Rotations Worksheet (PDF)

8th Grade math worksheet: Translations, Reflections and Rotations – Maths PDF

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This rigid transformations worksheet for 8th Grade covers translations, reflections and rotations (Common Core 8.G.A.1, 8.G.A.2, 8.G.A.3), with a free PDF to print.

These 20 problems practice translations, reflections, rotations and congruence on the coordinate plane (Common Core 8.G.A.1, 8.G.A.2 and 8.G.A.3). Each problem has its own space for work, so print the page and write directly on it.

The problems start with direct skill checks and grow harder as you go. Later items combine transformations and describe sequences of moves. Use the answer key afterwards to check every step.

Grade 8 · Common Core State Standards: 8.G.A.1, 8.G.A.2, 8.G.A.3

Rigid transformations worksheet: exercises 1 to 10

Exercise 1 – Translate a point

Slide the point \((-5, 4)\) right 6 and down 7. Give the image.

Exercise 2 – Translate a triangle

Triangle ABC.

Translate triangle \(ABC\) right 3 and down 2. List the image vertices.

Exercise 3 – Reflect across the x-axis

Reflect \((4, -3)\) across the x-axis.

Exercise 4 – Reflect across the y-axis

Reflect \((-5, 2)\) across the y-axis.

Exercise 5 – Reflect a triangle

Triangle PQR.

Reflect triangle \(PQR\) across the y-axis and list the image vertices.

Exercise 6 – Rotate 90 degrees counterclockwise

Turn the point \((4, -3)\) by \(90^{\circ}\) counterclockwise about the origin. Give the image.

Exercise 7 – Rotate 180 degrees

Rotate \((-3, 4)\) by \(180^{\circ}\) about the origin.

Exercise 8 – Rotate clockwise

Rotate \((3, 1)\) by \(90^{\circ}\) clockwise about the origin.

Exercise 9 – Rotate a triangle

Triangle DEF.

Rotate triangle \(DEF\) by \(90^{\circ}\) counterclockwise about the origin. Give the image vertices.

Exercise 10 – Identify the transformation

The point \(M(2, 6)\) is mapped to \(M^{\prime}(2, -6)\). Which transformation could this be?

Exercises 11 and up

Exercise 11 – Lengths are preserved

Segment \(AB\) has endpoints \(A(1, 1)\) and \(B(4, 1)\). After a translation 3 right and 2 down, what is the length of \(A^{\prime}B^{\prime}\)?

Exercise 12 – Properties preserved

A triangle with angles \(40^{\circ}\), \(60^{\circ}\) and \(80^{\circ}\) is reflected. What are the angles of the image? Explain.

Exercise 13 – Translation then reflection

Translate \((2, 3)\) right 4, then reflect the result across the x-axis.

Exercise 14 – Reflection then translation

Reflect \((-2, 1)\) across the y-axis, then translate it up 3.

Exercise 15 – Describe the sequence

Triangle ABC and its image.

Triangle \(A^{\prime}B^{\prime}C^{\prime}\) is the image of \(ABC\). Describe one transformation that maps \(ABC\) to \(A^{\prime}B^{\prime}C^{\prime}\).

Exercise 16 – Show congruence

Two triangles.

Show that the two triangles are congruent by describing a transformation.

Exercise 17 – Park statue

On a map of a park, a statue is at \((-4, 3)\) and the river runs along the y-axis. A matching statue is placed on the other side of the river as a mirror image. Where does it go?

Exercise 18 – Robot vacuum

A robot vacuum starts at \((2, 3)\) in a room map. It moves 5 units left and 4 units down. Where does it stop, and what transformation describes the move?

Exercise 19 – Logo rotation

A school logo has a vertex at \((4, 2)\). The logo is rotated \(90^{\circ}\) counterclockwise about the origin. Find the new location of the vertex.

Exercise 20 – Which changes orientation

Which transformations change the order of the vertices (the orientation) of a figure: translation, reflection or rotation? Explain.

Key facts behind this rigid transformations worksheet

Key facts

Translation by \((a, b)\): \((x, y) \to (x + a, y + b)\).
Reflection across the x-axis: \((x, -y)\); across the y-axis: \((-x, y)\).
Rotation about the origin: \(90^{\circ}\) counterclockwise \((-y, x)\); \(180^{\circ}\) \((-x, -y)\); \(90^{\circ}\) clockwise \((y, -x)\).
Rigid motions preserve lengths, angles and parallel lines.
Two figures are congruent if a sequence of rigid motions maps one to the other.

How to use this rigid transformations worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the rigid transformations worksheet as a PDF with the button below and keep it with your notes.

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