Unit 6 · Topic 1

Transformations

Overview

Slide, flip, and turn figures while keeping their size and shape.

Topic 1 of 3~22 min
Next: Dilations & SimilarityAll units
Unit overview

The lesson

Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

Three rigid transformations

  1. 1Translation: slide every point the same distance and direction.
  2. 2Reflection: flip across a line (a mirror image).
  3. 3Rotation: turn around a fixed point.
Worked example

Translate the point (2, 3) right 4 and down 1.

  1. 1Right 4: x goes from 2 to 6.
  2. 2Down 1: y goes from 3 to 2.
  3. 3New point: (6, 2).

Why this matters

Slide, flip, and turn figures while keeping their size and shape.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.

Re-reading the question too quickly. Underline what you are solving for before you start calculating.

Key ideas from this lesson

  1. Three rigid transformations
  2. Translation: slide every point the same distance and direction.
  3. Reflection: flip across a line (a mirror image).
  4. Rotation: turn around a fixed point.

Video walkthroughs

Khan Academy

Introduction to Transformations

Translations, reflections, and rotations explained.

Watch on YouTube
Other

Translations, Reflections, and Rotations

See rigid motions that preserve size and shape.

Watch on YouTube
Khan Academy

Identifying Scaled Copies

Distinguish rigid transformations from non-rigid ones.

Watch on YouTube
Khan Academy

Corresponding Parts of Scaled Copies

Match vertices and sides after a transformation.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

Translate point (3, 5) left 2 units and up 4 units.

Step-by-step solution

  1. 1Left 2: x = 3 − 2 = 1.
  2. 2Up 4: y = 5 + 4 = 9.
  3. 3Image: (1, 9).

Exercise 2

Try it yourself

Reflect (4, −2) across the x-axis.

Step-by-step solution

  1. 1x stays 4.
  2. 2y becomes the opposite: −(−2) = 2.
  3. 3Image: (4, 2).

Exercise 3

Try it yourself

Reflect (−3, 7) across the y-axis.

Step-by-step solution

  1. 1x becomes 3.
  2. 2y stays 7.
  3. 3Image: (3, 7).

Exercise 4

Try it yourself

Rotate (2, 0) 90° counterclockwise about the origin.

Step-by-step solution

  1. 1Apply rule: (−0, 2).
  2. 2Simplify coordinates.
  3. 3Image: (0, 2).

Exercise 5

Try it yourself

A triangle is translated 5 units right. Which property is preserved?

Step-by-step solution

  1. 1Translation is a rigid transformation.
  2. 2Side lengths and angle measures stay the same.
  3. 3The image is congruent to the original.

Re-read the lesson section if you get stuck, then try again without peeking at the solution.

Khan Academy

Transformations

Open resource
Math Worksheets 4 Kids

Transformation worksheets

Open resource

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Transformations

Question 1 of 4

Medium

Which transformation is NOT rigid (does not preserve size)?

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