Geometry Translations, Reflections and Rotations Test with Point Values (PDF)

Geometry math test: Translations, Reflections and Rotations – Maths PDF

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This geometry transformations test for Geometry covers translations, reflections and rotations (Common Core G-CO.A.2, G-CO.A.4, G-CO.A.5), with a free PDF to print.

This 45-minute test checks coordinate rules for translations, reflections and rotations and for rigid motions. It has 9 questions worth 20 points in total. Show every step of the work, label diagrams, and include units where they apply. Calculators are allowed unless the teacher says otherwise.

Time and points

About this test

Grade: Geometry
Chapter: Translations, Reflections and Rotations
Standards: G-CO.A.2, G-CO.A.4, G-CO.A.5
Time: 45 minutes
Total: 20 points

Geometry transformations test: questions

Question 1 – Translation [2 pts]

Triangle ABC.

Translate triangle ABC by the rule (x, y) → (x + 6, y − 5). Write the coordinates of A′, B′ and C′.

Question 2 – Reflection [2 pts]

Reflect (-5, 2) across the x-axis. (1 point)
Reflect (-5, 2) across the line y = x. (1 point)

Question 3 – Rotation [3 pts]

Rotate (3, 7) by 90° counterclockwise about the origin. (1 point)
Rotate (3, 7) by 180° about the origin. (1 point)
Rotate (3, 7) by 90° clockwise about the origin. (1 point)

Question 4 – Find the rule [2 pts]

A translation maps K(-2, 6) to K′(3, 1). Write the rule of the translation and use it to find the image of L(0, 0).

Question 5 – Identify the transformation [2 pts]

Segment ST and its image S′T′.

Name the rigid motion that maps ST to S′T′ and justify your answer with coordinates.

Question 6 – Composition [2 pts]

Point R.

Point R(4, -2) is reflected across the y-axis and then translated by (x, y) → (x + 1, y + 6). Find the final image.

Question 7 – Order matters [2 pts]

Point M(2, 1) is rotated 90° counterclockwise about the origin and then reflected across the x-axis. Another student reflects first and then rotates. Do the two students get the same image? Show the work.

Question 8 – Rigid motions [2 pts]

Triangle PQR has PQ = 5, QR = 12 and m∠Q = 90°. It is reflected and then translated. State PQ, QR and m∠Q for the image triangle and explain why.

Question 9 – Mirror line [3 pts]

The point (7, 4) is reflected across the vertical line x = 3 to give P′. Find P′, and find the distance between the point and P′.

Key facts behind this geometry transformations test

Key facts

A translation moves every point the same distance in the same direction: (x, y) to (x + a, y + b).
A reflection across the x-axis sends (x, y) to (x, -y); across the y-axis it sends (x, y) to (-x, y).
A 90 degree counterclockwise rotation about the origin sends (x, y) to (-y, x).
Rigid motions preserve distance and angle measure, so the image is congruent to the preimage.
When transformations are combined, the order matters.

How to use this geometry 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 Geometry chapters: Geometry math.

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