Vectors and Transfomations

Worked examples (14)extended set

• 1Magnitude of a combination of column vectors
• 2Dividing a line in a given ratio
• 3Midpoint proof: showing two lines are parallel
• 4Extending a line beyond a point
• 5Writing one vector in terms of two others
• 6Proving three points are collinear via a ratio
• 7Column vector arithmetic and magnitude
• 8Reading vectors from a grid and testing for parallel
• 9Vectors in a regular hexagon
• 10Where two lines in a parallelogram meet
• 11Points on a map grid from column vectors
• 12Magnitudes without a calculator
• 13Position vector of a midpoint in a trapezium
• 14Proving two sides are parallel inside a parallelogram

Worked examples (13)extended set

• 1Reflection in the line y = −x
• 2Rotation about a centre that is not the origin
• 3Finding the centre of an enlargement
• 4Two reflections in parallel lines
• 5Two reflections in perpendicular lines
• 6Negative fractional enlargement and its effect on area
• 7Translation and its inverse
• 8Describing a reflection and a rotation from a grid
• 9Reflection then rotation — and does order matter?
• 10Recovering a negative fractional enlargement
• 11Drawing a reflection and a rotation about a point
• 12Describing a translation and an enlargement from a grid
• 13A staircase of rotated rectangles