Question 2
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?
Try to draw it and verify if it is correct by taking some points on the curve and checking if their distances from P are indeed 4 cm. Explore, if you have not already done so, and see if a compass can be used for this purpose.
You can start by marking a few points of distance 4 cm from P using the compass. How can this be done?
All points at a fixed distance from a central point form a circle.
Step 1 — Mark the center point
Let us mark a point. We will call this point P. This is our starting point.
Step 2 — Find points at 4 cm distance
We need to mark points. These points must be 4 cm from P. Imagine a point Q, 4 cm to the right of P. Imagine a point R, 4 cm above P. Imagine a point S, 4 cm to the left of P. Imagine a point T, 4 cm below P. All these points are 4 cm away. If we mark points in all directions. They will form a smooth curve.
Step 3 — Use a compass to draw
A compass helps us draw this curve. First, we open the compass. We set its opening to this distance.
Place the compass needle on point P. Now, rotate the pencil end around P. The pencil draws a perfect circle. Every point on this circle is this distance from P. This circle shows all possible points.
Answer
(i) The points form a circle. (ii) The center of this circle is P. (iii) The radius of this circle is 4 cm.
More questions in A
Observe the following figures and try drawing them freehand.
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?
Try to draw it and verify if it is correct by taking some points on the curve and checking if their distances from P are indeed 4 cm. Explore, if you have not already done so, and see if a compass can be used for this purpose.
You can start by marking a few points of distance 4 cm from P using the compass. How can this be done?
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? Try again if you want to!
Also, has the use of instruments made the construction easier?
Construct
1. A Person
How will you draw this?
2. Wavy Wave
Construct this.
Make other artwork of your choice with a ruler and a compass.
Explore
How should the rectangle be constructed so that the diagonal divides the opposite angles into equal parts?
How will you record your observations? First, identify the parameters that need to be tracked. They are the sides of the rectangle and the 8 angles formed by the two diagonals. Are there any other measurements that you would want to keep track of?
In your experimentation, did you consider the case when all four sides of the rectangle are equal? That is, did you consider the case of a square? See what happens in this special case!
Math Talk
What general laws did you observe with respect to the angles and sides? Try to frame and discuss them with your classmates.
How can one be sure if the laws that you have observed will always be true?