Chapter 1.1, Problem 31PPSE

Solution

To determine the pattern and to draw the next three figures in the pattern given in the problem.

The next three figures of the pattern:

  

Given the pattern:

  

Calculation:

Observe that both the shapes execute a clockwise rotation.

When a shape is in the first row, it executes a square by square motion to its right side.

When, it is in the second row it executes a square by square motion to its left side.

In the last figure, the square is in the second row and the circle in in the first row.

Thus, the circle will move into the closest right square and the square will move into the closest left square.

Such a figure is drawn:

  

Now, since the square is in the second row and the circle is in the first row, the square will move into the closest left square and the circle will move into the closest right square during the next move.

Such a movement is drawn below:

  

Proceeding in a similar way, the next figure is also drawn:

  

Thus, the next three figures of the pattern

  

Conclusion:

The next three figures of the pattern