8th Grade Translations, Reflections and Rotations Test with Point Values (PDF)

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

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This rigid transformations test 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 20-point test checks translations, reflections, rotations and congruence on the coordinate plane (Common Core 8.G.A.1, 8.G.A.2 and 8.G.A.3). Work alone, show every step, and write each final answer clearly. You have 45 minutes. Calculators are not needed unless a question says so.

Time and points

About this test

Grade: Grade 8
Chapter: Translations, Reflections and Rotations
Standards: 8.G.A.1, 8.G.A.2, 8.G.A.3
Time: 45 minutes
Total: 20 points

Rigid transformations test: questions

Question 1 – Points [3 pts]

Translate \((5, -1)\) left 7 and up 3. (1 point)
Reflect \((-3, 6)\) across the x-axis. (1 point)
Rotate \((4, 1)\) by \(90^{\circ}\) counterclockwise about the origin. (1 point)

Question 2 – Translate a figure [3 pts]

Triangle KLM.

Translate triangle \(KLM\) 3 units right and 4 units down. List the image vertices.

Question 3 – Reflect a figure [3 pts]

Triangle WXY.

Reflect triangle \(WXY\) across the x-axis. List the image vertices.

Question 4 – Sequence [3 pts]

Triangle \(ABC\) has vertex \(A(2, 5)\). Find the image of \(A\) after a reflection across the y-axis followed by a translation 3 units down. Then find the image after a \(180^{\circ}\) rotation about the origin of the original point \(A\).

Question 5 – Properties [2 pts]

A rectangle is \(6\) cm by \(4\) cm. It is rotated \(90^{\circ}\). What are the dimensions of the image? Name two properties that stay the same.

Question 6 – Congruent figures [3 pts]

Two triangles.

Are the two triangles congruent? Describe a transformation that proves your answer.

Question 7 – Mirror [2 pts]

A point \(P(6, -2)\) is reflected across a line and its image is \(P^{\prime}(-6, -2)\). Name the line of reflection.

Question 8 – Explain [1 pt]

Explain in your own words why a reflection produces a figure congruent to the original even though the figure is flipped.

Key facts behind this rigid transformations test

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 test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 8 chapters: Grade 8 math.

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