Geometric Transformation Math Example 1
Follow the full solution, then compare it with the other examples linked below.
Example 1
easyName and describe the four basic geometric transformations.
Solution
- 1 Step 1: Translation — slides every point by the same vector : .
- 2 Step 2: Rotation — turns every point around a fixed center by a given angle.
- 3 Step 3: Reflection — flips every point over a line (the axis of reflection).
- 4 Step 4: Dilation — scales every point away from or toward a center by a scale factor .
Answer
Translation, Rotation, Reflection, Dilation.
Translation, rotation, and reflection are isometries — they preserve distances and angles (rigid motions). Dilation changes size but preserves shape (similarity transformation). Together these transformations form the foundation of geometric transformation theory.
About Geometric Transformation
A function that maps every point of a geometric figure to a new position, changing its location, orientation, or size.
Learn more about Geometric Transformation →More Geometric Transformation Examples
Example 2 medium
Point [formula] is reflected over the y-axis, then translated by [formula]. Find the final image.
Example 3 easyWhich geometric transformations are isometries (preserve distances)?
Example 4 hardShow that a 180° rotation about the origin is equivalent to the transformation [formula]. Verify wit