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Transformations (Cambridge (CIE) IGCSE Maths)

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    Define the term translation.

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  • Define the term translation.

    A translation is when a shape is moved.

    Its position changes but its size, shape and orientation stay the same.

  • What do you use to describe how a shape is moved horizontally and vertically by a translation?

    You use a vector in the form open parentheses table row x row y end table close parentheses to describe a translation.

    Within the vector, x describes the horizontal movement and y describes the vertical movement.

  • True or False?

    The vector open parentheses table row 2 row 3 end table close parentheses means 3 units to the right and 2 units up.

    False.

    The vector open parentheses table row 2 row 3 end table close parentheses does not mean 3 units to the right and 2 units up.

    The vector open parentheses table row 2 row 3 end table close parentheses means 2 units to the right and 3 units up.

    The top number is horizontal and the bottom number is vertical.

  • True or False?

    The vector open parentheses table row cell negative 2 end cell row 0 end table close parentheses means 2 units to the left.

    True.

    The vector open parentheses table row cell negative 2 end cell row 0 end table close parentheses means 2 units to the left.

  • True or False?

    The vector open parentheses table row 0 row cell negative 3 end cell end table close parentheses means 3 units up.

    False.

    The vector open parentheses table row 0 row cell negative 3 end cell end table close parentheses does not mean 3 units up.

    The vector open parentheses table row 0 row cell negative 3 end cell end table close parentheses means 3 units down.

    If the bottom number is negative it goes down.

  • How do you translate a shape?

    To translate a shape, move each corner according to the vector.

    Join the new corners together to make the translated shape.

  • True or False?

    When you translate a shape, it should not overlap with the original shape.

    False.

    When you translate a shape, it can overlap with the original shape.

  • To get full marks, what information do you need to give when describing a translation in an exam question?

    When describing a translation, you need to:

    • State that the transformation is a translation.

    • State the vector.

  • How do you reverse a translation?

    E.g. reverse a translation of open parentheses table row 6 row cell negative 2 end cell end table close parentheses.

    A translation can be reversed by changing the sign (but not the number) of each value in the translation vector, and moving the shape by this new vector.

    E.g. to reverse a translation of open parentheses table row 6 row cell negative 2 end cell end table close parentheses, move the translated shape by the vector open parentheses table row cell negative 6 end cell row 2 end table close parentheses.

  • What type of transformation is seen in the the diagram below?

    A diagram showing two identical objects on a grid in different positions. One is labelled A and the other is labelled B.

    The transformation in the diagram is a translation.

    The shape has moved position but has not changed in size or orientation.

    Shape A has been translated to shape B by the vector open parentheses table row 2 row cell negative 3 end cell end table close parentheses.

  • Define the term reflection.

    A reflection is when a shape is flipped about a line of symmetry.

    Its orientation changes and its position could change but its size stays the same.

  • True or False?

    A reflection in the line y equals 0 is always the same as a reflection in the y-axis.

    False.

    A reflection in the line y equals 0 is always the same as a reflection in the x-axis.

  • True or False?

    The line of reflection will always be horizontal or vertical.

    False.

    The line of reflection will not always be horizontal or vertical. It could be diagonal such as y equals x or y equals negative x.

  • Which points do not change when reflected?

    Any points that lie on the line of reflection do not change when reflected.

  • How do you reflect a shape about a line of reflection?

    To reflect a shape, reflect each corner separately.

    • Count or measure the perpendicular distance from a corner to the line of reflection.

    • Repeat this distance on the other side of the line.

    • Label the new corner.

    • Join all the corners up to form the reflected shape.

  • To get full marks, what information do you need to give when describing a reflection in an exam question?

    When describing a reflection, you need to:

    • State that the transformation is a reflection.

    • State the equation of the line of reflection.

  • True or False?

    To reverse a reflection, you can reflect it about the same line of reflection again.

    E.g. if an object has been reflected along the x-axis, then reflecting it along the x-axis again will bring it back to its initial position.

    True.

    To reverse a reflection, you can reflect it about the same line of reflection again.

  • What type of transformation is seen in the diagram below.

    A grid showing two shapes labelled A and B. The two shapes are the same size but are in different positions and a facing opposite each other.

    The transformation in the diagram is a reflection.

    The two shapes are the same size but are in different positions and orientations.

    Shape A has been reflected to shape B in the line x equals negative 1.

  • Define the term rotation.

    A rotation is when a shape is turned about a point.

    Its position could change but its size stays the same.

  • True or False?

    A rotation 90° clockwise is the same as a rotation 270° anticlockwise.

    True.

    A rotation 90° clockwise is the same as a rotation 270° anticlockwise.

  • True or False?

    You must state the direction of the rotation when the angle is 180°.

    False.

    You do not need to state the direction of the rotation when the angle is 180°. 180° clockwise is the same as 180° anticlockwise.

  • To get full marks, what information do you need to give when describing a rotation in an exam question?

    When describing a rotation, you need to:

    • State that the transformation is a rotation.

    • State the angle and direction of the rotation.

    • State the position of the centre of the rotation.

  • How do you rotate a shape about a centre of rotation?

    To rotate a shape about a centre of rotation:

    • Trace over the original shape.

    • Put your pencil on the centre of rotation.

    • Rotate the tracing paper by the given angle and in the given direction.

    • Draw the rotated shape as indicated by the tracing paper.

  • True or False?

    The centre of rotation can be inside the original shape.

    True.

    The centre of rotation can be inside the original shape.

  • What type of transformation is shown in the diagram below?

    A grid with two 'T' shapes labelled A and B. Shape A and B are identical but in different positions and have different orientations.

    The transformation in the diagram is a rotation.

    The shapes are identical but the positions and orientations are different.

    Shape A has been rotated by 90º in a clockwise direction about the centre (-4, 0) onto shape B.

  • Define the term enlargement.

    An enlargement is when a shape is stretched (or shrunk) both horizontally and vertically by the same factor.

  • True or False?

    Enlargements always make shapes bigger.

    False.

    Enlargements do not always make shapes bigger.

    The shape can be made smaller if the scale factor is between 0 and 1.

  • What does a scale factor of 3 mean in terms of enlargement?

    In terms of enlargement, a scale factor of 3 means that each edge of the enlarged image will be 3 times longer than the corresponding edge on the original object.

  • To get full marks, what information do you need to give when describing an enlargement in an exam question?

    When describing an enlargement, you need to:

    • State that the transformation is an enlargement.

    • State the scale factor.

    • State the coordinates of the centre of enlargement.

  • True or False?

    The centre of enlargement determines the position of the enlarged shape for a given scale factor.

    True.

    The centre of enlargement determines the position of the enlarged shape for a given scale factor.

    Moving the centre of enlargement will change the position of the enlarged image but it will not affect its size. It will still be enlarged by the same scale factor.

  • True or False?

    One of the corners of the enlarged shape is always on the centre of enlargement.

    False.

    One of the corners of the enlarged shape does not have to be on the centre of enlargement.

  • How do you enlarge a shape?

    To enlarge a shape:

    • Count/measure the distances from the centre of enlargement to a corner.

    • Multiply the distances by the scale factor.

    • Count the new distances from the centre of enlargement.

    • Repeat this for all the corners.

    • Join the corners together to form the enlarged shape.

  • True or False?

    If you draw a straight line that passes through a corner on the original shape and the corresponding corner on the enlarged shape, then that line will pass through the centre of enlargement.

    True.

    If you draw a straight line that passes through a corner on the original shape and the corresponding corner on the enlarged shape, then that line will pass through the centre of enlargement.

    This can be used to find the centre of enlargement or check your enlargements.

    These lines are sometimes called rays.

  • How do you find the scale factor of an enlargement?

    To find the scale factor of an enlargement, divide the length of any side on the enlarged shape by the length of the corresponding side on the original shape.

  • How do you find the centre of enlargement?

    To find the centre of enlargement, draw a straight line that passes through a corner on the original shape and the corresponding corner on the enlarged shape.

    Repeat this for one or more corners on the original shape.

    The point of intersection of these lines will be the centre of enlargement.

  • True or False?

    The scale factor of enlargement is the scale factor between the area of the original shape and the area of the enlarged shape.

    False.

    The scale factor of enlargement is not the scale factor between the area of the original shape and the area of the enlarged shape.

    It is the scale factor of their corresponding lengths, not their areas.

  • True or False?

    The scale factor of an enlargement must be greater than 1.

    False.

    The scale factor of an enlargement does not have to be greater than 1.

    If the scale factor is greater than 0 but less than 1, the enlarged image will be smaller than the original object.

    If the scale factor is less than 0 then the enlarged image will appear upside-down on the opposite side of the centre of enlargement to the original object.

  • How do you reverse an enlargement?

    E.g. reverse an enlargement of scale factor -2 about the centre of enlargement (3, 1).

    An enlargement can be reversed by performing another enlargement:

    • The centre of enlargement remains the same.

    • The scale factor is the reciprocal of the initial scale factor.

    E.g. to reverse an enlargement of scale factor -2 about the centre of enlargement (3, 1), perform another enlargement with scale factor negative 1 half about the centre of enlargement (3, 1).

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