Geometry Translations, Reflections and Rotations Worksheet Solutions (PDF)

Geometry math worksheet solutions: Translations, Reflections and Rotations – Maths PDF

Cover of the book Geometry Math Worksheets with Answers (PDF)

Download as a PDFThe Geometry worksheets book with answersPrintable PDFSee the book ›

Sommaire

This geometry transformations answers 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.

Use this answer key to check the 20 problems on transformations. Every solution shows the formula or theorem used, each step of the work, and the final answer in bold. If an answer differs from yours, compare the steps line by line to find where the work changed.

Geometry · Common Core State Standards: G-CO.A.2, G-CO.A.4, G-CO.A.5

Geometry transformations answers: exercises 1 to 10

Exercise 1 – Translate a point

\((3 + 4, -2 + 5) = (7, 3)\)

(7, 3)

Exercise 2 – Reflect across the x-axis

Change the sign of y.

\((5, -(-3)) = (5, 3)\)

(5, 3)

Exercise 3 – Reflect across the y-axis

Change the sign of x.

(4, 6)

Exercise 4 – Rotate 90 degrees

Use \((x, y) \text{ maps to } (-y, x)\).

\((-5, 2)\)

(-5, 2)

Exercise 5 – Rotate 180 degrees

Use \((x, y) \text{ maps to } (-x, -y)\).

(3, -4)

Exercise 6 – Translate a triangle

The image is 5 units left and 2 units up.

\(A^{\prime} = (1 – 5, 1 + 2) = (-4, 3)\)

\(B^{\prime} = (4 – 5, 1 + 2) = (-1, 3)\)

\(C^{\prime} = (2 – 5, 3 + 2) = (-3, 5)\)

A′(-4, 3), B′(-1, 3), C′(-3, 5)

Exercise 7 – Reflect a triangle

Change the sign of each y-coordinate.

\(D^{\prime}(-3, -2),\ E^{\prime}(-1, -5),\ F^{\prime}(-1, -2)\)

D′(-3, -2), E′(-1, -5), F′(-1, -2)

Exercise 8 – Rotate a triangle clockwise

Rotation of 90° clockwise.

A 90° clockwise turn equals a 270° counterclockwise turn: \((x, y) \text{ maps to } (y, -x)\).

\(A^{\prime}(1, -1),\ B^{\prime}(1, -4),\ C^{\prime}(3, -2)\)

A′(1, -1), B′(1, -4), C′(3, -2)

Exercise 9 – Reflect across y = x

Swap the coordinates.

(-7, 3)

Exercise 10 – Reflect across a vertical line

The point is 4 units right of the line, so the image is 4 units left of it.

\(2 – 4 = -2\)

(-2, 1)

Exercises 11 and up

Exercise 11 – Find the translation rule

\(-1 – 2 = -3\) and \(7 – 3 = 4\), so the rule is \((x, y) \text{ maps to } (x – 3, y + 4)\).

\(B^{\prime} = (0 – 3, -5 + 4) = (-3, -1)\)

(x – 3, y + 4); B′(-3, -1)

Exercise 12 – Identify the transformation

Each x-coordinate changes sign and each y-coordinate stays the same.

A reflection across the y-axis

Exercise 13 – Rotate 270 degrees

Use \((x, y) \text{ maps to } (y, -x)\).

\((-1, -4)\)

(-1, -4)

Exercise 14 – Reflect, then translate

\((3, 4) \text{ maps to } (3, -4)\)

\((3 + 2, -4 – 1) = (5, -5)\)

(5, -5)

Exercise 15 – Does the order matter?

\((3, 4) \text{ maps to } (5, 3) \text{ maps to } (5, -3)\)

The previous answer was (5, -5), so the order changes the result.

(5, -3); the order matters

Exercise 16 – Video game sprite

Path of the sprite.

After moving: \((6 – 4, 2 + 3) = (2, 5)\).

After the reflection across the y-axis: \((-2, 5)\).

(-2, 5)

Exercise 17 – Crane arm

New location: \((-6, 8)\).

Before: \(\sqrt{8^{2} + 6^{2}} = 10\). After: \(\sqrt{(-6)^{2} + 8^{2}} = 10\).

(-6, 8); the length stays 10 units

Exercise 18 – Floor tile

The tile and its 180° image.

Use \((x, y) \text{ maps to } (-x, -y)\) for each vertex.

(-1, -2), (-4, -2), (-5, -4), (-2, -4)

Exercise 19 – Two-step sequence

\((2, -3) \text{ maps to } (-2, -3)\) after the reflection.

\((-2, -3) \text{ maps to } (3, -2)\) after the rotation.

(3, -2)

Exercise 20 – Rigid motions keep distance

\(A^{\prime}(-2, 1)\) and \(B^{\prime}(-6, 4)\).

\(AB = \sqrt{3^{2} + 4^{2}} = 5\)

\(A^{\prime}B^{\prime} = \sqrt{(-6 + 2)^{2} + (4 – 1)^{2}} = \sqrt{16 + 9} = 5\)

Both lengths are 5 units

Key facts behind this geometry transformations answers

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 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 geometry transformations answers as a PDF with the button below and keep it with your notes.

All Geometry chapters: Geometry math.

Voter.. post

Free printable PDF