Page 215 - ICSE Math 8

¾ Reflection of a point (x, y) about y-axis is (–x, y).

¾ Reflection of a point (x, y) about origin is (–x, –y).
¾ Rotation is a transformation which rotates all the points in a plane about a fixed point through a given angle.
¾ The fixed point about which the rotation is made is known as the centre of rotation and the amount of
rotation is known as the angle of rotation.

¾ The image of a point (x, y) rotated about the origin through an angle of 180° is (–x, –y).
¾ The image of a point (x, y) rotated about the origin through an angle of 90° in anticlockwise direction is
(–y, x) and in clockwise direction is (y, –x).

¾ A geometrical figure is said to have rotational symmetry about a point if it coincides with its image at
least once before completing a full turn.
¾ The fixed point about which a figure is rotated is known as the centre of rotation and the number of times
the figure appears exactly the same during a 360° rotation is known as the order of rotational symmetry.

MENTAL MATHS

1. Write True or False.
(a) A square has only two lines of symmetry.

(b) The reflection of point (–5, 8) about y-axis is (5, –8).
(c) The image of point (p, q) when rotated about the origin through 180° is (–p, –q).

(d) A circle has finite number of lines of symmetry.
2. Complete the tables given below.

(a) Point Reflection about
x-axis y-axis origin
(2, 0) _____________ _____________ _____________
(0, 2) _____________ _____________ _____________

(–1, 3) _____________ _____________ _____________

Rotation about origin through an angle of
(b) Point 90° 90°
180°
(anticlockwise) (clockwise)
(1, 0) _____________ _____________ _____________
(–2, 3) _____________ _____________ _____________
(–3, –3) _____________ _____________ _____________

PRACTICE TIME

1. Draw the lines of symmetry (if possible) for the following figures.
(a) (b) (c) (d)

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