Page 236 - Ganit Kaushal

Construction 14: Construct a Wavy Wave, as shown in the figure, where the central line AB is of length 8 cm
and both the waves are half circles. (NCERT)
Sol. Follow the steps as under:

Step 1: Draw a straight line AB, 8 cm long, with the help of a ruler and pencil. A B
Our next step depends on the answer to the following two questions. Can you answer them?
What should be the length of AX, and what should be the radius of the half circles?
Great! You are absolutely right. AX is the diameter of the circular waves, and AX = BX.
So, AX should be 4 cm, and the radius is half of the diameter, so the radius of each wave is 2 cm.
Step 2: Set the compass to a radius of 2 cm, as shown in the adjoining figure (i). 2 cm
Step 3: Put the pointer at A, and draw an arc to cut the line AB at C. Likewise, put the pointer (i)
at B, and draw an arc to cut the line AB at D. (see figure (ii))
Step 4: Without changing the setting of the compass, X D B
put the pointer at C and draw an upper half circle. A C D B A C
Then put the pointer at D and draw a lower half circle.
This gives the figure of Wavy Waves as shown in (ii) (iii)
figure (iii). Remove all the supporting arcs and points, and shade it a little with a pencil to get a good-
looking wavy wave.
Construction of Wavy Waves when Waves are Smaller than a Half Circle

Construction 15: Construct a Wavy Wave where the central line AB is of length 8 cm and both the waves are
smaller than half circles.
Step 1: Draw a straight line AB, 8 cm long. Mark a point X on it, 4 cm away X
from A, with the help of a ruler and pencil. X is the midpoint of A and B. A B
Our next step depends on the answer to the following questions. Can you answer this?
How can we make waves smaller than half circles?
Excellent! You are right. We can do this by making the radius of waves more than 2 cm and taking the
centre of the circular waves on opposite sides of the central line, not on the central line, as we did in
our previous construction.
Step 2: Set the distance between the legs of the compass to more than 2 cm. For conformity, let us
take it as 3 cm. Put the pointer at A and draw an arc. Again, put the pointer at X, and draw another arc
to cut the previous arc at C. D D

Likewise, put the pointer at B and X one by one and
draw two arcs to cut each other at the point D, as
shown in the figure (i). A X B A X B
It is obvious that the point C is equidistant from A
and X, and point D is equidistant from B and X.
Step 3: Without changing the settings of the compass, C C
put the pointer at C, and draw an arc from A to X. (i) (ii)
Now, put the pointer at D and draw an arc from B to X, as shown in the figure (ii).
Step 4: After removing all the supporting arcs and points, we get the final A X B
figure of wavy waves where the waves are smaller than half circles, as shown (iii)
in the adjoining figure (iii).
[Students are advised to recreate wavy waves by taking the central lines of different lengths. The
more you practise, the better you will become.]

234 Mathematics-6