Path Tracing

Tracking path endpoints through grid rotations and reflections.

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Tracking path endpoints through grid rotations and reflections.

Path tracing combines path following with spatial transformation. Given a path on a grid and a transformation (rotation or reflection), you must determine where the path ends after the transformation is applied. This tests the ability to mentally transform coordinate systems.

new_endpoint = transform(path_endpoint, transformation)

Path ending at top-right, rotated 90° clockwise: ends at bottom-right
Path mirrored horizontally: x-coordinates flip
180° rotation: both x and y coordinates invert

How to recognize it

First identify the path's endpoint before transformation
Apply the rotation or reflection to that specific point
For rotation: track how corners of the grid move
For mirror: flip coordinates across the axis

Common mistakes

Confusing rotation direction (clockwise vs counterclockwise)
Applying transformation to wrong reference point
Forgetting to transform relative to grid center

Step-by-step walkthrough

A path on a 4x4 grid starts at bottom-left (●) and ends at top-right (★). After rotating the entire grid 90° clockwise, where does the path end?

Find the path endpoint: the ★ is at the top-right corner of the grid.
For 90° clockwise rotation: imagine turning the grid like a steering wheel to the right.
The top edge of the grid becomes the right edge. The right edge becomes the bottom edge.
So the top-right corner moves to the bottom-right corner.

Answer: The path ends at the bottom-right corner

Practice guidance

Spatial Reasoning