Why do this problem?
This activity enables learners to explore the concept of gradient
and it follows on nicely from Perpendicular
. The lengths of the sides of the square being equal
connects with Pythagoras Theorem and the property that, for
perpendicular lines the product of the gradients is -1 (reversing
the horizontal and vertical increments).
The problem can be used in the early stages of working on gradients
and before introducing the equation of a straight line in 2D. At
this stage it will be challenging for the majority of learners and
take up most of a lesson.
Although it is tagged as Stage 3, the problem can also be used at
Stage 4 or 5 when it could be completed in 10 to 15 minutes.
At Stage 5, extension work
could ask for the equation of the circle through the 4 vertices
linking Pythagoras Theorem, the midpoint of a line segment, the
distance between 2 points with given coordinates and the equation
of a circle.
If you know the coordinates of two points how much do you go up and
down on the line through the points when you go across one
How do you know if 2 line segments are parallel?
How do you know if 2 line segments are perpendicular?
If you know the coordinates of two points how do you find the
distance between them?
Questions for the Stage 5
How do you find the midpoint of a square?
What do you know about points on a circle in relation to the centre
of the circle?