Why do this problem?
allows students to explore the connections between
straight lines on graphs and the equations that represent or define
them - equations of the form $y = mx + c$.
Take time to discuss how an equation represents a line by defining
the set of points that lie along it. If this needs some
reinforcement the related problem Parallel
might be a good place to start.
Show the interactivity, moving all four points to allow the group
to see the freedoms the lines have. Draw attention to the equations
of the lines showing beneath the graph.
Ask a student to move the lines so that they are perpendicular.
Does everyone agree? How can we be sure? Can anyone set up a harder
pair of perpendicular lines? Are they correct? Preliminary work
looking at perpendicular lines is suggested in At
Ask students to work in pairs at computers, finding pairs of
perpendicular lines and noting their equations. What do they notice
about the equations of perpendicular lines? Encourage them to make
and test their conjectures. Bring the class together to share
insights and conclusions.
When they understand what is going on, ask them to set challenges
for each other - either for their partner, or on the board for the
e.g. find three pairs of perpendicular lines which go through
$(2,3)$, find perpendicular lines where one goes through $(-1,3)$
and the other through $(6,2)$...
What does perpendicular mean?
How do the equations of perpendicular lines relate to each other
and why is that?
Ask students to suggest equations for sets of fourlines that define
a rectangle/square/parallelogram, etc. This is described in the
. It would be useful to have graph plotting software
Concentrate on the work in Parallel
When discussing perpendicularity, ask students to draw tilted
squares on the interactivity in Square
, and/or to do some work drawing them on squared
paper. This topic might also provide a good excuse to play the game