Question 2

We will draw a wave on a straight line using two half-circles.

Step 1 — Draw the central line

First, let us draw a straight line segment. Let us call the start of this line point A. Let us call the end of this line point B. The length of this line segment AB is 12 cm.

Step 2 — Find the middle point

We need to divide the line AB into two equal parts. We find the exact middle point of the line AB. Let us call this middle point X. So, the line AB is now split into two parts: AX and XB. The length of AX is half of the total length AB.

$AX = \frac{AB}{2}$

$AX = \frac{12 \text{ cm}}{2}$

$\boxed{AX = 6 \text{ cm}}$

The length of the other part, XB, is also 6 cm.

Step 3 — Calculate the radius for the half-circles

Our wave will be made of two half-circles. The first half-circle will use AX as its diameter. The second half-circle will use XB as its diameter. To draw a half-circle with a compass, we need to know its radius. The radius is always half of the diameter.

For the first half-circle, the diameter is AX = 6 cm. Its radius will be:

$Radius_1 = \frac{AX}{2}$

$Radius_1 = \frac{6 \text{ cm}}{2}$

$\boxed{Radius_1 = 3 \text{ cm}}$

For the second half-circle, the diameter is XB = 6 cm. Its radius will be:

$Radius_2 = \frac{XB}{2}$

$Radius_2 = \frac{6 \text{ cm}}{2}$

$\boxed{Radius_2 = 3 \text{ cm}}$

So, both half-circles will have a radius of 3 cm.

Step 4 — Draw the first half-circle

We will draw the first half-circle on the segment AX. The radius is 3 cm. The center of this half-circle is the middle point of AX. Let us call this center $C_1$. Place the sharp point of your compass at $C_1$. Open the compass so the pencil tip is 3 cm away from the sharp point. Draw a half-circle above the line segment AX. This half-circle starts at point A and ends at point X.

Step 5 — Draw the second half-circle

Now, we will draw the second half-circle on the segment XB. The radius is also 3 cm. The center of this half-circle is the middle point of XB. Let us call this center $C_2$. Place the sharp point of your compass at $C_2$. Open the compass to 3 cm. Draw a half-circle below the line segment XB. This half-circle starts at point X and ends at point B. It goes in the opposite direction to the first half-circle. This completes our wave on the central line AB.

Answer

(i) The length of the central line AB is 12 cm. (ii) The radius for the first half-circle is 3 cm. (iii) The radius for the second half-circle is 3 cm.