Challenge Level

On the grid below, join the two blue dots, A and B, together with a
straight line.

Now join the green dots, C and D, with a straight line.

Now join the green dots, C and D, with a straight line.

At what angle do the two lines cross?

Investigate the number of squares "along" and "down" from A to
B compared with the number of squares "along" and "up" from C to D.
What do you notice?

Using what you have found out, can you draw lines that are
perpendicular (at $90^{\circ}$) to the lines drawn below?

Is there only one solution each time?

Do the two lines have to be the same length? Why or why
not?