Select a suitable figure from the four alternatives that would complete figure…

Concept

In this figure-matrix, every cell is built from straight lines that run from one or more corners of the square to its centre. Reading across a row, the third figure is obtained by comparing the first two figures and removing whichever corner-to-centre line is common to both; only the lines that belong to just one of the two figures carry over.

Application

1. The first figure in the third row is a single line running from the bottom-left corner to the top-right corner, straight through the centre.

2. The second figure in that row is a peak sitting on the bottom edge, made of a line from the bottom-left corner to the centre and a second line from the bottom-right corner to the centre.

3. The bottom-left-to-centre line appears in both figures, so it is the common part and drops out.

4. What is left is the centre-to-top-right line (found only in the first figure) and the centre-to-bottom-right line (found only in the second figure).

5. Putting these two remaining lines together gives a figure whose two arms meet at the centre and open out towards the top-right and bottom-right corners only.

Cross-check

The same rule checks out on the earlier rows. In row two, the first figure already has centre-lines to the bottom-left, top-right and bottom-right corners, and the second figure is the plain diagonal from the top-left corner to the bottom-right corner. The centre-to-bottom-right line is common to both and is dropped, leaving centre-lines to the top-left, top-right and bottom-left corners — exactly the third figure that is already drawn in that row. Since the rule reproduces every given figure correctly, the missing figure in row three must be the alternative whose two lines meet at the centre and reach only the top-right and bottom-right corners.

The rule also reproduces row one: the first figure there is a short line from the centre to the bottom-right corner only, and the second figure is a chevron made of a centre-to-top-left line and a centre-to-bottom-left line. Neither figure shares a line with the other, so nothing is common and nothing drops out — the third figure keeps all three lines (centre-to-bottom-right, centre-to-top-left and centre-to-bottom-left), which is exactly the third figure already drawn in row one.