Orientation Math Example 4
Follow the full solution, then compare it with the other examples linked below.
Example 4
hardA left-handed glove is reflected in a mirror. Can the reflected image be rotated in 3D to match the original left-handed glove?
Solution
- 1 Step 1: Reflecting a left-handed glove gives a right-handed glove.
- 2 Step 2: In 3D, rotations preserve orientation — a right-handed glove rotated in any direction remains right-handed.
- 3 Step 3: The reflected image has opposite orientation and cannot be superimposed on the original by any rotation.
Answer
No. The reflected glove is right-handed and cannot be rotated to match the left-handed original.
This is a classic chirality example. Left and right hands are mirror images (enantiomorphs) that cannot be superimposed by rotations in 3D. Reflection reverses the 'handedness' (orientation), and no rotation can undo this reversal. In chemistry, this concept applies to chiral molecules.
About Orientation
Orientation is the directional sense of a geometric figure — whether its vertices are ordered clockwise or counterclockwise. It describes how a shape is 'facing' in space, and is preserved by rotations and translations but reversed by reflections.
Learn more about Orientation →More Orientation Examples
Example 1 easy
A triangle has vertices listed counterclockwise as A, B, C. After a reflection, the vertices appear
Example 2 mediumVertices of triangle ABC are at [formula], [formula], [formula]. Using the signed area formula, dete
Example 3 easyDoes a 90° rotation change the orientation of a figure?