Page 205 - ICSE Math 7

Angle of rotation

The minimum angle through which an object or a figure rotates about a fixed point to coincide with
itself is known as the angle of rotation. An object is said to take a full turn if it rotates by 360°.
A half-turn means a rotation by 180° and a quarter-turn means a rotation by 90°.

Rotation of a point
Let A be a point which is to be rotated anticlockwise about a point O through
an angle of 60°. To do so, follow the steps given below.
A
Step 1: Join OA.
B
O A'
Step 2: Construct ∠AOB = 60°.
Step 3: With O as centre, cut OA' = OA on ray OB. A
A' is the new position of A after a rotation of 60°.
60°
O
Rotation of a line segment
Let AB be a line segment which is to be rotated clockwise around a point O
through an angle of 90°. To rotate the line about O, follow the steps given below. A

Step 1: Join OA and OB. B
A O

Step 2: Construct ∠AOC = 90° and ∠BOD = 90°.
Step 3: With O as centre, cut OA' = OA on ray OC and OB' = OB on B
ray OD. O A'

Step 4: Join A'B'. C
A'B' is the new position of line segment AB after a clockwise
rotation of 90° about point O.
B'
D
Rotation of a triangle A
Let ABC be a triangle which is to be rotated clockwise around a point O through C
an angle of 180° (half turn). To do so, follow the steps given below. B
A O

Step 1: Join OA, OB and OC. B C
A
O
Step 2: Construct ∠AOD = 180°, ∠BOE = 180° and ∠COF = 180°. B C
Step 3: With O as centre, cut OA' = OA on ray OD, cut OB' = OB on O 180°
ray OE and cut OC' = OC on ray OF. C' B'
Step 4: Join A'B', B'C' and C'A' to get DA'B'C'. DA'B'C' is the new E
position of DABC after rotation of 180° about point O. F A'
D

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