Copyright © University of Cambridge. All rights reserved.

'Dotty Relationship' printed from http://nrich.maths.org/

Show menu

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.

grid with four dots marked
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?

line connecting points by 3 along and 3 up
line connecting points by 4 along 1 down
line connecting points by 1 along 3 down
Is there only one solution each time?

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