The following question is taken from my website Diagnostic Questions. Here you will find 1000s of high quality maths multiple choice diagnostic / hinge questions, ideal for assessment for learning, which have been created and shared by maths teachers all over the world.

This question was created by one of the delegates at the 2014 TSM Maths Conference where I ran a series of workshops on the effective use of Autograph in the maths classroom.

I set my group of delegates a “homework” activity to create 3 diagnostic questions each using Autograph. I thought this would be a good way to test out their new found skills, and also getting them thinking about other ways to use the software.

The advantage of designing a diagnostic question on a dynamic graphing package (the same is true of Desmos or GeoGebra) is that once the question has been asked, answered and discussed, there is opportunity for further discussion and investigation by firing up the original graph file itself.

With the question above, once students have established how to work out the equation of the perpendicular line, there is perfect opportunity to ask questions such as:

If I moved Point A one square up, what would the equation of the green line be?

Where could I move Points A and B so that the equation of the green line was y = -2x + 1?

Can you give me the equation of two perpendicular lines that cross the x-axis at (-4, 0)?

The possibilities are endless, and it reinforces my view that it is far better to plan questions than tasks. Here you have a really great question for assessing students’ understanding of gradients and the equation of perpendicular lines, and then a fantastic opportunity to extend their understanding further.