Right and up are positive

The idea

Distances from O are marked off in equal units on both axes; distances to the right of O or upwards from O are positive, and distances to the left of O or downwards from O are negative.

Left or right?

Reiaan starts at O. First he walks 3 units right along the x-axis. Back at O, he walks 3 units left. Both walks are 3 units long, so the numbers must tell the two places apart.

Which number should name the spot 3 units to the left of O?

• 3
• −3
• 0

Walk from O

Both axes use equal units. Move P to each place and read its numbers.

Which way?

Distances from O are marked off in equal units on both axes. To the right of O or up from O they are positive. To the left of O or down from O they are negative.

• Move from O | Sign | Example
• Right (x-axis) | + | 4 units right → 4
• Left (x-axis) | − | 3 units left → −3
• Up (y-axis) | + | 2 units up → 2
• Down (y-axis) | − | 5 units down → −5

Notes

Right and up are positive. Left and down are negative. Distances from O use equal units on both axes.

Check yourself

The point marked −4 on the x-axis is…

A point on the y-axis is 6 units below O. What number marks it?

Answer: -6

Down from O is negative, so the point is −6.

Which of these places has a negative number?

On the x-axis, how many units to the left of O is the point −7?

Answer: 7

The minus sign says "left". The point is 7 units from O.

• 4 units to the right of O. Right of O is positive. −4 is on the other side.
• 4 units to the left of O — correct. Yes. Left of O is negative, so −4 is 4 units to the left.
• 4 units above O. Above and below belong to the y-axis. The x-axis goes left and right.
• 2 units right of O. Right of O is positive.
• 2 units up from O. Up from O is positive.
• 2 units left of O — correct. Yes. Left of O is negative: −2.