Playing with Constructions | FIO

Question 3

Try to recreate the figure where the waves are smaller than a half circle (as appearing in the neck of the figure, 'A Person'). The challenge here is to get both the waves to be identical. This may be tricky!

Question diagram 1
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Solution

Let us draw the figure step by step.

Step 1 — Draw the body

First, we draw a rectangle. Let its width be 6 cm. Let its height be 5 cm. Mark the top-left corner as C. Mark the top-right corner as D. Mark the bottom-left corner as A. Mark the bottom-right corner as B.

Rectangle width: 6 cm, height: 5 cm\boxed{\text{Rectangle width: 6 cm, height: 5 cm}}

Diagram 1

Step 2 — Mark the neck point

Find the middle point of the top side CD. Let us call this point E. E is 3 cm from C. E is also 3 cm from D.

Midpoint E is 3 cm from C and D\boxed{\text{Midpoint E is 3 cm from C and D}}

Diagram 2

Step 3 — Draw the neck and head

From point E, draw a straight line upwards. Let this line be 2 cm long. Mark the top end of this line as F. Point F is the center of the head. Now, draw a circle with center F. Let the radius of this circle be 2 cm.

Neck length: 2 cm, Circle radius: 2 cm\boxed{\text{Neck length: 2 cm, Circle radius: 2 cm}}

Diagram 3

Step 4 — Draw the curved neck lines

These are two identical curves. They connect C to E and E to D. We will use a compass for this. Open your compass to 2 cm. For the curve from C to E: Place the compass point at C. Draw a small arc above the line CE. Now, place the compass point at E. Draw another small arc above the line CE. These two arcs will cross each other. Let us call this crossing point O1O_1. O1O_1 is the center for our first curve. With O1O_1 as center, draw an arc. Use a radius of 2 cm. This arc connects C to E. For the curve from E to D: Place the compass point at E. Draw a small arc above the line ED. Now, place the compass point at D. Draw another small arc above the line ED. These two arcs will cross each other. Let us call this crossing point O2O_2. O2O_2 is the center for our second curve. With O2O_2 as center, draw an arc. Use a radius of 2 cm. This arc connects E to D. These curves are smaller than a half circle. The radius is 2 cm. Half the distance CE is 1.5 cm. The radius is bigger than this.

Arc radius: 2 cm\boxed{\text{Arc radius: 2 cm}}

Diagram 4

Answer

(i) The figure is recreated by following the steps. (ii) The body is a rectangle of 6 cm width and 5 cm height. (iii) The head is a circle of 2 cm radius. (iv) The neck curves are arcs of 2 cm radius.

More questions in FIO

Q1

What radius should be taken in the compass to get this half circle? What should be the length of AX?

Q2

Take a central line of a different length and try to draw the wave on it.

Q3

Try to recreate the figure where the waves are smaller than a half circle (as appearing in the neck of the figure, 'A Person'). The challenge here is to get both the waves to be identical. This may be tricky!

Q4

Draw the rectangle and four squares configuration (shown in Fig. 8.3) on a dot paper.

What did you do to recreate this figure so that the four squares are placed symmetrically around the rectangle? Discuss with your classmates.

Q5

Identify if there are any squares in this collection. Use measurements if needed.

Q6

Think: Is it possible to reason out if the sides are equal or not, and if the angles are right or not without using any measuring instruments in the above figure? Can we do this by only looking at the position of corners in the dot grid?

Q7

Draw at least 3 rotated squares and rectangles on a dot grid. Draw them such that their corners are on the dots. Verify if the squares and rectangles that you have drawn satisfy their respective properties.

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