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Step 3: Now, draw a perpendicular to line Step 4: Now, using a ruler, open the compass to
AB at point B. Let us call this line m. take the radius of 7 cm, and from A, mark an arc
cutting line m at C. Join AC.
m
m
C

7 cm

A 4 cm B
A 4 cm B
m
Step 5: Now, construct perpendiculars to AB and BC at points A and C D C
respectively. The point where these perpendiculars intersect is the fourth
point.
7 cm
Thus, ABCD is a rectangle with side AB = 4 cm and diagonal AC = 7 cm.

A 4 cm B
create and solve
How to convert a square into a rectangle?
We can use the following steps to solve the challenge:
• Draw a square on a piece of paper and cut it diagonally through its centre.
This will create two triangular sections, say ABC and ADC.
• Now, take one of the resulting triangular sections (say, ABC) and cut it in half.
This will give two smaller triangular sections., say ABE and BEC.
• Place the two smaller triangular sections (ABE and BEC) obtained from the
second cut along the remaining triangular section (ADC).
• Adjust their placement so that all the sections fit together to form a new
quadrilateral ACFG as shown here.
• Check that the quadrilateral created by the rearranged sections is a rectangle.
Thus, this procedure effectively changes a square into a rectangle.
Explore how to convert a rectangle into a square.

Points Equidistant from Two Given Points

To locate the points that are equidistant from two given points, follow these steps:

Step 1: Mark the two given points (say, A and B) on your notebook.

A B
Step 2: To locate points that are at an equal distance from both A and B.
• Take a compass and open it little more than half of the distance between A and B. Then,
place the metal tip at A and draw a circle with A as the centre.

245 Playing with Constructions