Geometric Transformation Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
easyWhich geometric transformations are isometries (preserve distances)?
Solution
- 1 Step 1: An isometry preserves the distance between any two points.
- 2 Step 2: Translation, rotation, and reflection all preserve distances — they are isometries.
- 3 Step 3: Dilation changes distances (unless ) — it is not an isometry.
Answer
Translation, rotation, and reflection are isometries.
Isometries are the rigid motions of geometry — they preserve the shape and size of figures. Dilation preserves shape but not size, making it a similarity transformation rather than an isometry. Every isometry of the plane is a combination of at most three reflections.
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 1 easy
Name and describe the four basic geometric transformations.
Example 2 mediumPoint [formula] is reflected over the y-axis, then translated by [formula]. Find the final image.
Example 4 hardShow that a 180° rotation about the origin is equivalent to the transformation [formula]. Verify wit