Draw perpendicular lines from each of the mid-points.For example, A rotation of 60° = an anticlockwise rotation of 60° A rotation of –90° = an clockwise rotation of 90° Explain why a rotation of 120° is equivalent to a rotation of –240°.įinding the centre of rotation Find the point about which A is rotated onto its image A’. A negative rotation is an clockwise rotation. If this is the case then we use the following rules: A positive rotation is an anticlockwise rotation. For example, 90° O Rotating this shape 90° anticlockwise about point O produces the following image.ĭetermining the direction of a rotation Sometimes the direction of the rotation is not given. Rotating shapes The centre of rotation can also be inside the shape. The image triangle A’B’C’ is congruent to triangle ABC. Rotating shapes If we rotate triangle ABC 90° clockwise about point O the following image is produced: B object 90° A A’ image B’ C C’ O A is mapped onto A’, B is mapped onto B’ and C is mapped onto C’. This is the fixed point about which an object moves. To describe a rotation we need to know three things: ĭescribing a rotation A rotation occurs when an object is turned around a fixed point. Draw lines from any two vertices to their images.Reflecting shapes A A’ B B’ object image C C’ D D’ mirror line or axis of reflection If we draw a line from any point on the object to its image, the line forms a perpendicular bisector to the mirror line.įinding a line of reflection Construct the line that reflects shape A onto its image A’. A’ B’ object image C’ D’ mirror line or axis of reflection The image is congruent to the original shape. Reflecting shapes A B C D If we reflect the quadrilateral ABCD in a mirror line, we label the image quadrilateral A’B’C’D’. For example, Each point in the image must be the same distance from the mirror line as the corresponding point of the original object. Reflection An object can be reflected in a mirror line or axis of reflection to produce an image of the object. We can find the order of rotational symmetry using tracing paper. Only objects that have rotational symmetry of two or more are said to have rotational symmetry. If the order of rotational symmetry is one, then the object has to be rotated through 360° before it fits onto itself again. The order of rotational symmetry is the number of times the object fits onto itself during a 360° turn. Rotational symmetry An object has rotational symmetry if it fits exactly onto itself when it is turned about a point at its centre. one line of symmetry four lines of symmetry no lines of symmetry The mirror line is called a line of symmetry. Reflection symmetry If you can draw a line through a shape so that one half is the mirror image of the other then the shape has reflection or line symmetry.
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