Lessons · Teaching · the coordinate plane
Along the corridor, then up the stairs
A point on the coordinate plane is named by an ordered pair: the first number is the horizontal position along the x axis, the second is the vertical position along the y axis. The order is fixed, and (3, 5) is a different point from (5, 3).
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Every graph a pupil ever reads depends on this, and the error is always the same: reading the pair backwards. 'Along the corridor, then up the stairs' is worth more than any explanation, because it survives the two years until they need it again.
How to think about it
Start at the origin, which is (0, 0). Move along the horizontal axis by the first number, then vertically by the second. Negative means the other way. State the quadrant if asked, counting anticlockwise from the top right.
Worked example
(3, 5): three right from the origin, then five upAlong first, up second. Always in that order.
(-2, 4) is two left and four up, in the top left quadrantA negative first number sends you left, not down.
(3, 5) and (5, 3) are different pointsWhich is the whole meaning of the word 'ordered' in ordered pair.
The distance between (1, 2) and (1, 7) is 5, read straight off the y valuesSame x, so the points are on a vertical line and the difference is the distance.
Your turn
Name which axis the first number of a coordinate pair belongs to.
The first number is the position along the axis
Solve one, graded on the server
The trap
Reading a graph's pair in the order it happens to be labelled on the page. The convention is x then y regardless of which label is printed first.