Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.
I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
Drawing a triangle is not always as easy as you might think!
In abstract and computer generated art, a real object can be represented by a simplified set of lines. Can you create a picture using mathematical instructions?
Can you make sense of the three methods to work out the area of the kite in the square?