Skip to content

Geometric Transformations

Perform translations, reflections, rotations, and dilations on the coordinate plane.

Written and reviewed by the Study Mondo Education TeamLast updated
🎯⭐ INTERACTIVE LESSON

Try the Interactive Version!

Learn step-by-step with practice exercises built right in.

Start Interactive Lesson →

Geometric Transformations

Types of Transformations

Translation (Slide)

Every point moves the same distance in the same direction.

(x,y)→(x+a,y+b)(x, y) \to (x + a, y + b)

Translate right 3, up 2: (x,y)→(x+3,y+2)(x, y) \to (x + 3, y + 2)

Reflection (Flip)

A mirror image across a line.

ReflectionRule
Over x-axis(x,y)→(x,−y)(x, y) \to (x, -y)
Over y-axis(x,y)→(−x,y)(x, y) \to (-x, y)
Over y=xy = x(x,y)→(y,x)(x, y) \to (y, x)

Rotation (Turn)

Turn around a center point (usually the origin).

Rotation about originRule
90°90° counterclockwise(x,y)→(−y,x)(x, y) \to (-y, x)
180°180°(x,y)→(−x,−y)(x, y) \to (-x, -y)
270°270° counterclockwise(x,y)→(y,−x)(x, y) \to (y, -x)

Dilation (Resize)

Enlarge or shrink by a scale factor kk from a center point.

(x,y)→(kx,ky)(x, y) \to (kx, ky)

  • k>1k > 1: enlargement
  • 0<k<10 < k < 1: reduction

Rigid Transformations (Congruence)

Translations, reflections, and rotations are rigid — they preserve:

  • Size (lengths)
  • Shape (angles)
  • Congruence

Similarity Transformations

Dilations change size but preserve shape. Combined with rigid transformations, they create similar figures.

Congruence vs. Similarity

  • Congruent: Same shape AND same size (rigid transformations)
  • Similar: Same shape, possibly different size (dilation + rigid)

Coordinate practice: Triangle with vertices (1,2),(3,4),(1,4)(1,2), (3,4), (1,4). Reflect over the y-axis to get (−1,2),(−3,4),(−1,4)(-1,2), (-3,4), (-1,4).

Explain using:
🎴

Practice with Flashcards

Rate this topic's cards with spaced repetition. Cards join your deck when you finish a topic's lesson and take its exit quiz.

📖

Browse All Topics

Explore more Grade 8 Math topics

❓ Frequently Asked Questions

What is Geometric Transformations?▾
Perform translations, reflections, rotations, and dilations on the coordinate plane.
How can I study Geometric Transformations effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Regular review and active practice are key to retention.
Is this Geometric Transformations study guide free?▾
Yes — all study notes, flashcards, and practice problems for Geometric Transformations on Study Mondo are free to access. No account is needed.
What course covers Geometric Transformations?▾
Geometric Transformations is part of the Grade 8 Math course on Study Mondo, specifically in the Transformations section. You can explore the full course for more related topics and practice resources.