The figure has two components — a circle with a short line (the head and neck) and a square-like body whose top side is replaced by a curve that dips inwards.
Steps of construction
Draw the body first. Draw a line segment DE = 4 cm for the base.
At D and at E draw perpendiculars of length 4 cm and mark the top corners B and C. (Do not join B and C by a straight line.)
Now the curve. Take a radius of about 2.5 cm in the compass, place the tip above the middle of BC, and try it out until the pencil passes through both B and C. Draw that arc — it dips down into the body.
Above the arc, draw a short vertical line segment of about 1 cm for the neck, starting from the lowest point of the arc.
With the top of the neck as the point of contact, draw a circle of radius 1.5 cm for the head.
A Person. The red dot is where the compass tip is placed; the dashed lines show that it is the same distance from B and from C. The red curve through B and C is the part that is actually drawn.
Why the tip goes above the body: an arc always bends away from the compass tip. To make the top of the body sink downwards, the centre must be placed above it. Move the tip higher and the curve becomes flatter; bring it lower and the curve becomes deeper.
Q2.
Wavy Wave. Construct this. (As the length of the central line is not specified, we can take it to be of any length. Let us take AB to be the central line such that the length of AB is 8 cm. Here, the first wave is drawn as a half circle.)
Answer
Steps of construction
Draw a line segment AB = 8 cm. This is the central line.
Mark its mid-point X, so that AX = XB = 4 cm.
Mark the mid-point of AX; it is 2 cm from A. Place the compass tip there, open it to 2 cm and draw a half circle above AB from A to X.
Without changing the opening, place the tip at the mid-point of XB (2 cm from X) and draw a half circle below AB from X to B.
Rub out nothing — the two half circles together make one smooth wave.
The wavy wave on AB = 8 cm. The two red dots are where the compass tip is placed; both half circles have radius 2 cm.
Why the radius is 2 cm: each half circle sits on half of AB, that is on a diameter of 4 cm. Radius is half of the diameter, so radius = 4 ÷ 2 = 2 cm.