Geometric Invariance Math Example 3

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Example 3

easy
A rectangle is translated 5 units right and 3 units up. Name two properties that are invariant and one that is NOT invariant under this translation.

Solution

  1. 1
    Step 1: Translation is an isometry — it moves every point by the same vector without rotation or reflection. Therefore side lengths and angle measures are preserved (invariant).
  2. 2
    Step 2: The coordinates of every vertex shift by (+5,+3)(+5, +3), so vertex coordinates are NOT invariant.

Answer

Invariant: side lengths, angle measures. Not invariant: vertex coordinates.
Translations preserve all metric properties (distance, angles, area, perimeter) because the figure moves rigidly. Only position-dependent quantities such as coordinates change.

About Geometric Invariance

A property or measurement of a geometric figure that remains unchanged when a particular transformation is applied.

Learn more about Geometric Invariance →

More Geometric Invariance Examples

Example 1 medium

A triangle is reflected across the [formula]-axis and then rotated [formula] counterclockwise about

Example 2 hard

Under a dilation with scale factor [formula] centred at the origin, a circle has centre [formula] an

Example 4 hard

The cross-ratio of four collinear points is [formula], an invariant under projective transformations

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