8th Grade Translations, Reflections and Rotations Worksheet Solutions (PDF)
This rigid transformations answers 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.
This answer key gives a full worked solution for each of the 20 problems on the translations, reflections and rotations worksheet (Common Core 8.G.A.1, 8.G.A.2 and 8.G.A.3). Compare each step with your own work, not only the final answer, and note any step where your method differed.
Grade 8 · Common Core State Standards: 8.G.A.1, 8.G.A.2, 8.G.A.3
Rigid transformations answers: exercises 1 to 10
Exercise 1 – Translate a point
Add 6 to x and \(-7\) to y: \((-5 + 6, 4 – 7)\).
\((1, -3)\)
Exercise 2 – Translate a triangle
\((x, y) \to (x + 3, y – 2)\).
\(A^{\prime}(4, -1),\ B^{\prime}(7, -1),\ C^{\prime}(4, 1)\)
Exercise 3 – Reflect across the x-axis
The x-coordinate stays the same and the y-coordinate changes sign.
\((4, 3)\)
Exercise 4 – Reflect across the y-axis
The y-coordinate stays the same and the x-coordinate changes sign.
\((5, 2)\)
Exercise 5 – Reflect a triangle
\((x, y) \to (-x, y)\).
\(P^{\prime}(-1, 2),\ Q^{\prime}(-4, 2),\ R^{\prime}(-1, 5)\)
Exercise 6 – Rotate 90 degrees counterclockwise
\((x, y) \to (-y, x)\), so \((4, -3) \to (3, 4)\).
\((3, 4)\)
Exercise 7 – Rotate 180 degrees
\((x, y) \to (-x, -y)\).
\((3, -4)\)
Exercise 8 – Rotate clockwise
\((x, y) \to (y, -x)\), so \((3, 1) \to (1, -3)\).
\((1, -3)\)
Exercise 9 – Rotate a triangle
\((x, y) \to (-y, x)\).
\(D^{\prime}(0, 1),\ E^{\prime}(0, 3),\ F^{\prime}(-2, 3)\)
Exercise 10 – Identify the transformation
The x-coordinate is unchanged and the y-coordinate changes sign.
A reflection across the x-axis
Exercises 11 and up
Exercise 11 – Lengths are preserved
\(AB = 3\). The image has endpoints \((4, -1)\) and \((7, -1)\), so its length is \(7 – 4 = 3\).
3 units, the same length
Exercise 12 – Properties preserved
A reflection is a rigid transformation, so angle measures are preserved.
40°, 60° and 80°
Exercise 13 – Translation then reflection
Translate: \((6, 3)\). Reflect: \((6, -3)\).
\((6, -3)\)
Exercise 14 – Reflection then translation
Reflect: \((2, 1)\). Translate: \((2, 4)\).
\((2, 4)\)
Exercise 15 – Describe the sequence
Each vertex \((x, y)\) goes to \((-x, -y)\).
A rotation of 180° about the origin
Exercise 16 – Show congruence
Compare: \((0, 0) \to (5, 1)\), \((2, 0) \to (7, 1)\), \((0, 3) \to (5, 4)\). Every point moves 5 right and 1 up.
A translation 5 right and 1 up maps one onto the other, so they are congruent
Exercise 17 – Park statue
Reflect across the y-axis: change the sign of the x-coordinate.
\((4, 3)\)
Exercise 18 – Robot vacuum
\((2 – 5, 3 – 4) = (-3, -1)\).
\((-3, -1)\); a translation
Exercise 19 – Logo rotation
\((x, y) \to (-y, x)\), so \((4, 2) \to (-2, 4)\).
\((-2, 4)\)
Exercise 20 – Which changes orientation
A reflection flips the figure like a mirror, reversing the order of the vertices. Translations and rotations keep the order.
Only reflections
Key facts behind this rigid transformations answers
- 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 answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
Download the rigid transformations answers as a PDF with the button below and keep it with your notes.
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