Monday Maths: Vicki Robinson, Communications Officer
A #MondayMaths enlargement entrapment
We’re stretching your knowledge of enlargement in this week’s #MondayMaths. The challenge is to contain a rectangle inside the biggest and smallest possible enlargements of a second rectangle.
This is a tricky problem but works well in Year 10 for challenging the higher attainers in your class.
Year 10 students will be looking at enlargement this term and if they are confident working with and understanding points of enlargement, this is a perfect depth exercise.
Students can be encouraged to recognise that any maximally or minimally large enlargement of ABCD that still completely contains rectangle EFGH will have sides that coincide with one or more of the sides of EFGH.
They should also be familiar with the rays of enlargement that extend from the point M.
To add depth to this puzzle, you could ask students to give the scale factor of the enlarged rectangles that they have formed. This could result in some fractional enlargements.
You could also ask “how would the size of the largest or smallest rectangle change if we moved the rectangle EFGH closer towards ABCD?”
Pencils at the ready
A good start is to pencil in these rays to identify the permitted points on which the vertices of any enlarged shape.
Students should also try extending the sides of EFGH to meet the rays of enlargement.
Think carefully about where EFGH is allowed to sit. For example, the point E cannot lie above or left of the equivalent of point A in the enlarged rectangle.
Geogebra: a free online geometry tool – and a great resource for experimenting with this problem!
How did your class get on with this? Share your thoughts on Twitter where we’ll be posting our answer on Thursday.