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What Are You Plotting?

Investigate the positions of points which have particular x and y coordinates. What do you notice?

Dotty Relationship

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Dotty Relationship

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?

Why do this problem?

This problem could be linked to coordinates. It could also form an introduction to vectors at a higher level. It is a powerful geometrical investigation. It has the potential to quickly lead to generalisations that pupils can apply in the second part of the question.

Possible approach

The notion of "how long is a line?" would form an excellent discussion point in the plenary.

Key questions

Possible extension

Possible support