Symmetry | A

Question 2

Ink Blot Devils

Take a piece of paper. Fold it in half. Open the paper and spill a few drops of ink (or paint) on one half.

Now press the halves together and then open the paper again.

  • What do you see?
  • Is the resulting figure symmetric?
  • If yes, where is the line of symmetry?
  • Is there any other line along which it can be folded to produce two identical parts?
  • Try making more such patterns.
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Solution

The ink blot experiment shows how folding creates a mirror image.

Step 1 — Making the Ink Blot

We take a piece of paper. We fold it in half. We open the paper. We spill some ink drops. We put them on one half. We press the halves together. Then we open the paper again.

Diagram 1

Step 2 — Observing the Pattern

We see a unique pattern. It looks like a strange creature. It could be a butterfly. It could be a monster. One side of the pattern is like the other. It is a mirror image.

Step 3 — Checking for Symmetry

Yes, the resulting figure is symmetric. We can fold the paper again. We fold it along the original fold line. The two halves of the pattern match perfectly. They lie exactly on top of each other.

Step 4 — Finding the Line of Symmetry

The line of symmetry is the fold line. This is the line where we first folded. It divides the pattern into two parts. These parts are mirror images.

Step 5 — Looking for Other Lines of Symmetry

Usually, there is no other line. The ink was placed randomly. It was only on one side. So, only the fold line works. It is very rare to find another. This needs a special ink shape.

Step 6 — Making More Patterns

We can try making more patterns. Each one will be unique. Each one will show symmetry. It is a fun way to explore.

Answer

(i) We see a unique pattern. It looks like a mirror image. (ii) Yes, the resulting figure is symmetric. (iii) The line of symmetry is the original fold line. (iv) Usually, no, there is no other line. (v) We can make many more unique patterns.

More questions in A

Q1

Does a square have only one line of symmetry? Take a square piece of paper. By folding, find all its lines of symmetry.

Q2

Ink Blot Devils

Take a piece of paper. Fold it in half. Open the paper and spill a few drops of ink (or paint) on one half.

Now press the halves together and then open the paper again.

  • What do you see?
  • Is the resulting figure symmetric?
  • If yes, where is the line of symmetry?
  • Is there any other line along which it can be folded to produce two identical parts?
  • Try making more such patterns.
Q3

Use thin rectangular coloured paper. Fold it several times and create some intricate patterns by cutting the paper, like the one shown here. Identify the lines of symmetry in the repeating design.

Q4

Trace and cut out a copy of this figure. By rotating the cutout over this figure determine its angles of rotation.

Q5

Game

Draw a 6 by 6 grid. Two players take turns covering two adjacent squares by drawing a line. The line can be placed either way: horizontally or vertically. The lines cannot overlap. The game goes on till a player is not able to place any more lines. The player who is not able to place a line loses.

With what strategy can one play to win this game?

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