Page 237 - Ganit Kaushal

 In the above 2 constructions, the length of the central line was given.

Can we construct wavy waves for any arbitrary length of the central line AB?
Yes, we can. For this, we need the help of construction 4 (perpendicular bisector of a line).

Construction of Wavy Waves with an Arbitrary Central Line
Construction 16: Construct wavy waves for any arbitrary length of the central line AB. Both the waves are
half-circles.
Sol. Follow the given steps:

Step 1: Draw a straight line AB of any arbitrary length with the help of a ruler A B
and a pencil. X
Step 2: Draw the perpendicular bisector of the line AB [use construction 4]. A B
It passes through point X, the midpoint of A and B [see figure (i)]. (i)
Step 3: Now, draw the perpendicular bisectors of AX and BX [use construction X
4]. These perpendicular bisectors cut AX and BX at points C and D, respectively. A C (ii) D B
Therefore, C and D are the midpoints of AX and BX, respectively [see
figure (ii)]. X B
Step 4: Taking C as the centre and AC as the radius, draw a half circle on A C D
the upper side of line AB. It will pass through X. Likewise, taking D as the
centre and BD as the radius, draw a half circle on the lower side of line AB. (iii)
It will also pass through X.
Step 5: Now, after removing all the supporting lines, arcs and points, we A X B
get the final figure of wavy waves, where both the waves are half circles, as
shown in figure (iv). (iv)
4. A Person

Let us learn how to construct the artwork ‘A Person’.

The adjoining figure, titled ‘A Person’, is a combination of three geometrical shapes – a circle, an
arc and straight lines in the shape of a rectangle.

Construction 17: Draw ‘A Person’ by making a good estimate of measurements according to your
wisdom. (NCERT)

Sol. To draw ‘A Person’, follow the given steps:
Step 1: Draw a horizontal straight line AB, 4 cm long. At points A and B, draw D C
perpendiculars AD and BC, respectively, each 4 cm long with the help of a protractor,
ruler and pencil (as explained in Step 2 of construction 5). The result should look like
the figure shown in figure (i). A (i) B
Step 2: Draw the perpendicular bisector OP of line DC, by fixing a
distance of 3 cm between the pointer and pencil lead of a compass. O
Then, OD = OC = 3 cm. Now with O as the centre and OD as the O
radius, draw the arc DC. The resulting figure is shown in figure (ii). D C D C
Step 3: With O as the centre and taking a radius equal to 1.5 cm,
draw a full circle. P
Step 4: Join point O to the midpoint of AB, but keep only the part A B A B
lying between arc DC and the circle. Remove all the supporting (ii) (iii)
points and arcs. We get the required final figure of the artwork ‘A Person’ as shown in figure (iii).

Playing with Constructions 235