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5 Vectors and transformation geometry

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  1. 5.1 Vectors

    1. 5.1.HAVector magnitude and direction

      Understand that a vector has both magnitude and direction.

    2. 5.1.HBVector notation and column vectors

      understand and use vector notation, including column vectors and notation for the vector from O to A and the vector a

    3. 5.1.HCMultiply vectors by scalar quantities

      multiply vectors by scalar quantities

    4. 5.1.HDAdd and subtract vectors

      add and subtract vectors

    5. 5.1.HEMagnitude of a vector

      calculate the modulus (magnitude) of a vector

    6. 5.1.HFResultant vectors

      find the resultant of two or more vectors

    7. 5.1.HGVector methods for simple geometrical proofs

      apply vector methods for simple geometrical proofs

  2. 5.2 Transformation geometry

    1. 5.2.ASpecifying rotations

      Understand that a rotation is specified by a centre and an angle.

    2. 5.2.BRotate a shape about a point through a given angle

      rotate a shape about a point through a given angle

    3. 5.2.CPositive and negative rotations

      recognise that an anti-clockwise rotation is a positive angle of rotation and a clockwise rotation is a negative angle of rotation

    4. 5.2.DReflection in a mirror line

      understand that reflections are specified by a mirror line Such as x = 1, y = 2, y = x, y – x = 0

    5. 5.2.EConstructing mirror lines and reflections

      Construct a mirror line from an object and its image, and reflect a shape in a given mirror line.

    6. 5.2.FTranslation by distance and direction

      understand that translations are specified by a distance and direction

    7. 5.2.GTranslate a shape

      translate a shape

    8. 5.2.HColumn vectors in translations

      understand and use column vectors in translations

    9. 5.2.IRigid transformations and congruence

      Understand that rotations, reflections and translations preserve lengths and angles, so the image remains congruent to the original.

    10. 5.2.JSpecifying enlargements

      Understand that an enlargement is specified by a centre and a positive scale factor, including fractional scale factors.

    11. 5.2.KAngle and length effects of enlargement

      Understand that enlargements preserve angles but do not generally preserve lengths.

    12. 5.2.LEnlarge a shape given the scale factor With or without

      enlarge a shape given the scale factor With or without a centre given

    13. 5.2.MComplete descriptions of transformations

      Identify transformations and give complete descriptions of them.