Identifying the Matrix Pattern

To find the missing figure, we need to identify the logical rule governing the 3x3 grid. The pattern can be found by analyzing the relationship between the figures in each row.

The rule is that the figure in the third column is a superposition (a combination of all the lines) of the figures in the first and second columns.

Verifying the Pattern

Let's count the horizontal (H) and vertical (V) lines to check this rule.

• Row 1:
  (Figure 1: 3H, 1V) + (Figure 2: 1H, 3V) = (Figure 3: 4H, 4V).
  This is correct.
• Row 3:
  (Figure 1: 2H, 2V) + (Figure 2: 2H, 2V) = (Figure 3: 4H, 4V).
  This is also correct.

Applying the Pattern to Find the Missing Cell

Now, we apply the same rule to the second row to find the missing figure.

• Figure 1: 2 Horizontal lines, 2 Vertical lines (2H, 2V).
• Missing Figure (?): Let's say it has 'x' horizontal and 'y' vertical lines (xH, yV).
• Figure 3: 3 Horizontal lines, 3 Vertical lines (3H, 3V).

Setting up the equation:

(2H, 2V) + (xH, yV) = (3H, 3V)

Solving for the number of lines:

• For horizontal lines: 2 + x = 3 → x = 1.
• For vertical lines: 2 + y = 3 → y = 1.

The missing figure must have 1 horizontal line and 1 vertical line.

Conclusion

Looking at the options provided, the figure labeled 3 is the only one with exactly one horizontal and one vertical line. Therefore, it is the correct figure to fill the missing cell.