Practice Cartesian coordinate system
A coordinate system locates points using ordered coordinates along perpendicular axes.
It lets you describe positions and represent relationships with graphs.
Exercises with solutions
A coordinate system has two axes: the horizontal x-axis and the vertical y-axis. They meet at the origin (0|0). Every point is given as a pair (x|y), first the value on the x-axis, then the value on the y-axis.
Exercise 1
In which order do you read a point (x|y)?
Show solution and working
x first, then y
The first number belongs to the horizontal axis, the second to the vertical. Memory aid: walk first, then climb.
Exercise 2
How do you find the point (3|2)?
Show solution and working
3 right, 2 up
The 3 belongs to the x-axis, so three units right. The 2 belongs to the y-axis, so two units up.
Exercise 3
How do you find the point (−2|4)?
Show solution and working
2 left, 4 up
A negative x means to the left. The y is positive, so upwards.
Exercise 4
Which point lies on the y-axis: (0|5) or (5|0)?
Show solution and working
(0|5)
On the y-axis the x value is zero. The point (5|0) lies on the x-axis instead.
Common mistake
Swapping the order and reading y first. (3|2) and (2|3) are two different points. Also watch the direction when values are negative.
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