2. Wavy Wave Construct this.

Question

Homi · Accepted Answer

Understand the Question

The task is to construct a wavy wave pattern using geometric tools. The design consists of a horizontal baseline with two connected, alternating semicircles (one curving above the baseline and one curving below) filled with vertical line shading.

Step 1 · Draw the Baseline and Mark Points

Draw a straight horizontal baseline. Diagram 1

Mark a starting point $A$ on the line.
Measure $4\text{ units}$ to the right of $A$ and mark point $B$ .
Measure another $4\text{ units}$ to the right of $B$ and mark point $D$ .

Step 2 · Draw the First Semicircle Above the Line

Find the center and construct the upper semicircle. Diagram 2

Find the midpoint of segment $AB$ : $\text{Radius} = \dfrac{4\text{ units}}{2} = 2\text{ units}$
Mark this midpoint as $C_1$ .
Place the compass needle at $C_1$ , set the radius to $2\text{ units}$ (reaching point $A$ ), and draw a semicircle above the line from $A$ to $B$ .

Step 3 · Draw the Second Semicircle Below the Line

Find the center and construct the lower semicircle. Diagram 3

Find the midpoint of segment $BD$ : $\text{Radius} = \dfrac{4\text{ units}}{2} = 2\text{ units}$
Mark this midpoint as $C_2$ .
Place the compass needle at $C_2$ , set the radius to $2\text{ units}$ (reaching point $B$ ), and draw a semicircle below the line from $B$ to $D$ .

Step 4 · Draw Vertical Shading Lines

Fill both semicircles with evenly spaced vertical lines. Diagram 4

Mark equally spaced points along segment $AB$ and draw vertical lines upwards until they touch the upper semicircle.
Mark equally spaced points along segment $BD$ and draw vertical lines downwards until they touch the lower semicircle.

Answer

The wavy wave pattern is constructed using two alternating semicircles of radius $2\text{ units}$ filled with vertical lines.

Common Mistakes

Drawing on the Same Side: Drawing both semicircles on top of the baseline instead of alternating one above ( $AB$ ) and one below ( $BD$ ) to create the wave.
Radius Error: Using the full segment length ( $4\text{ units}$ ) as the compass radius instead of halving it to find the radius ( $2\text{ units}$ ).

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