A line of symmetry is defined as a line that divides a figure into two parts in a waysuch that each part is a mirror image of the other part about that line.The given figure consists of 16 unit squares arranged as shown. In addition to thethree black squares, what is the minimum number of squares that must be colouredblack, such that both PQ and MN form lines of symmetry? (The figure isrepresentative)(A) 3(B) 4(C) 5(D) 6MNPQ

To determine the minimum number of squares that must be colored black in order for both PQ and MN to form lines of symmetry, we need to analyze the given figure.

First, let's identify the line of symmetry for PQ. PQ is a horizontal line passing through the middle of the figure. To maintain symmetry, any square above this line must have a corresponding mirror image square below the line. Similarly, any square below the line must have a corresponding mirror image square above the line.

Next, let's identify the line of symmetry for MN. MN is a vertical line passing through the middle of the figure. To maintain symmetry, any square to the left of this line must have a corresponding mirror image square to the right of the line. Similarly, any square to the right of the line must have a corresponding mirror image square to the left of the line.

Now, let's count the number of squares that need to be colored black to maintain symmetry.

For PQ to form a line of symmetry, we need to color the three black squares already present in the figure. These squares are already symmetrically placed with respect to PQ.

For MN to form a line of symmetry, we need to color additional squares. Looking at the figure, we can see that there are two squares to the left of MN that do not have corresponding mirror image squares to the right of MN. Similarly, there are two squares to the right of MN that do not have corresponding mirror image squares to the left of MN. Therefore, we need to color these four squares black to maintain symmetry for MN.

Adding up the squares needed for PQ and MN, we have a total of 3 + 4 = 7 squares that must be colored black.

However, the question asks for the minimum number of squares that must be colored black. We can observe that if we color the square at the top left corner black, it will automatically create symmetry for both PQ and MN. Therefore, we can reduce the number of squares that need to be colored black to 6.

Hence, the correct answer is (D) 6.