Identify the figure that completes the pattern.

Concept

In this kind of figure-completion item, the four quadrants of the grid are linked in diagonal pairs: the pattern in one quadrant, rotated 180 degrees about the centre of the whole grid, produces the pattern in the quadrant diagonally opposite it. A 180-degree rotation maps each quadrant's own corners to a fixed corner of its diagonal partner - a quadrant's own top-left corner corresponds to its partner's own bottom-right corner, and a quadrant's own top-right corner corresponds to its partner's own bottom-left corner (and vice versa in each case). So a line drawn between two of a quadrant's own corners reappears, in its diagonal partner, between the corresponding pair of that partner's own corners - the same diagonal family, just anchored to the corresponding corners - and any kink positioned close to one corner stays close to the corresponding corner after the rotation.

Application

1. The top-left quadrant's line runs between its own bottom-left corner (the mid-point of the grid's left edge) and its own top-right corner (the mid-point of the grid's top edge), with a stepped kink close to its own bottom-left corner.

2. The bottom-right quadrant is diagonally opposite the top-left quadrant. Under the rotation, the top-left quadrant's own bottom-left corner corresponds to the bottom-right quadrant's own top-right corner, and the top-left quadrant's own top-right corner corresponds to the bottom-right quadrant's own bottom-left corner.

3. So the bottom-right quadrant's line must run between its own bottom-left corner (the mid-point of the grid's bottom edge) and its own top-right corner (the mid-point of the grid's right edge) - the same diagonal family as the top-left quadrant's line - with its kink close to the corner that corresponds to the top-left quadrant's kink corner, that is, close to its own top-right corner.

Cross-check

Checking the four candidate figures: two of them show a line between their own top-left and bottom-right corners - a different diagonal family altogether - and are eliminated immediately, since a 180-degree rotation never changes which diagonal family a line belongs to. Of the remaining two, both show the correct diagonal family (their own bottom-left to top-right corners), but only one places its kink close to its own top-right corner, matching the required correspondence; the other places its kink close to its own bottom-left corner instead and is eliminated on that basis.

The figure with the bottom-left-to-top-right diagonal whose kink sits close to its own top-right corner is the one that completes the pattern.