Observe the way a compass is made. What can one draw with the compass? Explore!
Answer
A compass has two arms joined at a hinge — one arm ends in a sharp metal tip and the other holds a pencil. Once you tighten the hinge, the gap between the tip and the pencil lead cannot change while you turn it.
Press the metal tip on the paper and turn the pencil once round — you get a circle.
Turn it only part of the way — you get an arc (a piece of a circle).
Because the opening stays fixed, a compass can also copy a length from one place to another without a ruler.
Why it happens: the tip stays at one point and the pencil is always the same distance away from it. So every point the pencil draws is at that same distance from the tip — and that is exactly what a circle is.
Q2.
Mark a point ‘P’ in your notebook. Then, mark as many points as possible, in different directions, that are 4 cm away from P. Think: Imagine marking all the points of 4 cm distance from the point P. How would they look?
Answer
Do it like this:
Mark a point and name it P.
Place the ruler with its 0 mark on P, turn it to the right, and put a dot at the 4 cm mark.
Turn the ruler a little — up, sideways, slanting, downwards — and each time put a dot at 4 cm.
Keep going. The dots slowly form a ring around P.
If all such points are marked, they form a circle with centre P and radius 4 cm.
Every dot is 4 cm from P. Mark enough of them and the dots join up into a circle of radius 4 cm.
Why it happens: “4 cm from P” does not fix a direction — only a distance. Since you may go in any direction, the points spread evenly all around P, and a curve with every point at the same distance from a fixed point is a circle.
Q3.
You can start by marking a few points of distance 4 cm from P using the compass. How can this be done?
Answer
Place the ruler on the table. Put the metal tip of the compass at the 0 mark and open the compass until the pencil point reaches the 4 cm mark.
Tighten the screw so that the opening does not change.
Press the metal tip on the point P in your notebook.
Let the pencil touch the paper and make a small mark. Lift, turn the compass a little, and mark again — as many times as you like.
Now, keeping the tip fixed at P, turn the pencil all the way round without lifting it. You get the full circle.
Tip: Hold the compass only by the knob at the top and lean it slightly in the direction you are turning. Do not press the pencil hard, or the tip will slip and the circle will come out uneven.
Q4.
Take a point on the circle. What will be its distance from P— equal to 4 cm, less than 4 cm or greater than 4 cm? Similarly, what will be the distance between P and another point on the circle?
Answer
Its distance from P is exactly equal to 4 cm — not less, not more. The same is true for any other point you pick on the circle: every point of the circle is 4 cm from P.
distance from P to any point of the circle = radius = 4 cm
Why it happens: while you were drawing, the metal tip never moved from P and the compass opening never changed. So the pencil was always 4 cm away from P — and the curve it traced is made only of such points. P is called the centre and this fixed distance is called the radius.
Check it yourself: mark any three points on your circle and measure each one from P with a ruler. All three readings will be 4 cm.
Q5.
Having explored the use of a compass, go ahead and recreate the images in Fig. 8.1. Can you make the figures look as good as the figures shown there? Also, has the use of instruments made the construction easier?
Answer
Yes — with a compass the figures of Fig. 8.1 become easy, because every one of them is made only of circles.
Figure in Fig. 8.1
How to construct it
Two touching circles
Take radius 2 cm. Draw the first circle with centre A. Mark B on the line through A, 4 cm from A, and draw the second circle. They touch at exactly one point.
Circle inside a circle
Keep the tip at the same centre. Draw one circle of radius 1 cm and another of radius 2 cm.
Three overlapping circles
Mark three centres on one straight line, 2.5 cm apart, and draw a circle of radius 2 cm at each.
The mouse face
One big circle of radius 3 cm for the face; two circles of radius 1.5 cm for the ears, with their centres on the big circle; small circles for the eyes and nose; a straight line for the mouth.
The crossed sticks
Draw two slanting line segments crossing each other, then a small circle of radius 1 cm at the lower end of each.
Yes, the instruments make it far easier. Freehand circles come out wobbly and of different sizes; a compass gives a smooth curve, and the same opening gives circles of exactly the same size — so the picture looks neat and can be repeated.
Try This: keep one compass opening (say 2 cm) and, without changing it, draw six circles whose centres lie on one circle of the same radius. You get the beautiful six-petal rangoli flower.