What will happen if you do it once more? How many parallel lines will you get? Class 7

What will happen if you do it once more? How many parallel lines will you get? Class 7

Question 1.

What will happen if you do it once more? How many parallel lines will you get? Is there a pattern? Check if the pattern extends further, if you make another horizontal fold.

Solution:

We will get 9 parallel lines.

Yes. Pattern is: 2, 3, 5, 9, 17, ...

That is 2, 2 × 1 + 1, 2 × 2 + 1, 2 × 4 + 1, 2 × 8 + 1, i.e., 2, 2 × 2⁰ + 1, 2 × 2¹ + 1, 2 × 2² + 1, 2 × 2³ + 1, ..., 2 × 2ⁿ + 1. Thus, the pattern extends further, if we make another horizontal fold.

Question 2.

Make a vertical fold in the square sheet. This new vertical line is __________ to the previous horizontal lines. Class 7

Solution:

perpendicular

Question 3.

Fold the sheet along a diagonal. Can you find a fold that creates a line parallel to the diagonal line? Class 7

Solution:

Yes, by folding the paper along a line passing through the mid-points of two adjacent sides of the paper.