bouncing

this task is from 'five triangles'

what is the gradient of the line so that when a ball bounces (perfectly elastically of course) twice it then hits the mid-point of the lower side of the square?

some variety of techniques can be used and it doesn't involve higher mathematical techniques

• trigonometry isn't needed 
• it can be helpful to have some previous consideration about what happens to the gradient of a line when it is reflected
• or some consideration of when triangles are similar
• or you could solve this, very neatly, by working with the 'principle of reflections'

having solved this task, there are some obvious extensions:

students could also consider the length of the path(s)