Exercise 8.1 Solutions

Think (Page 188)

Question: Imagine marking all the points of 4 cm distance from the point P. How would they look?

Answer: They would form a Circle. If you mark infinite points exactly 4 cm away from a center $P$, they connect to form a perfect circular boundary.

Figure it Out (Page 191)

Q1. What radius should be taken in the compass to get this half circle? What should be the length of AX?

Answer:

• From the diagram, the total length of the central line $AB$ is 8 cm.
• The wave is made of two identical semicircles.
• The diameter of the first semicircle ($AX$) covers half the total length.
• $AX = 4$ cm.
• The Radius is half of the diameter ($AX$).
• Radius = $4 \div 2 = 2$ cm.

Q2. Take a central line of a different length and try to draw the wave on it.

Solution Steps:

1. Draw a line $AB$ of length, say, 10 cm.
2. Mark the midpoint $X$ at 5 cm.
3. Find the midpoint of $AX$ (at 2.5 cm). This is the center of the first upper semicircle.
4. Draw a semicircle upwards from $A$ to $X$ with radius 2.5 cm.
5. Find the midpoint of $XB$ (at 7.5 cm from A). This is the center of the second lower semicircle.
6. Draw a semicircle downwards from $X$ to $B$ with radius 2.5 cm.

Q3. Try to recreate the figure where the waves are smaller than a half circle.

Solution: This requires finding the correct radius and centers by trial and error or geometric construction (arcs intersecting). Specifically, the center of the arc must be lower than the line $AX$ to create a shallow wave, not a full semicircle.