The axes, the origin and the ordered pair (x, y). The x-coordinate is the signed distance from the y-axis, and the y-coordinate is the signed distance from the x-axis.
Draw two perpendicular lines across a plane. The horizontal line is the x-axis. The vertical line is the y-axis. Together they are the coordinate axes. The plane is called the Cartesian plane, the coordinate plane, or the xy-plane.
The axes cross at the origin, written O. Equal units are marked along both axes, starting from O. Distances to the right of O and above O are positive. Distances to the left and below are negative.
Which distance is which. The x-coordinate of P is its distance from the y-axis. The y-coordinate is its distance from the x-axis. The names cross over, and that is the most common source of mistakes.
Point P is 3 units from the y-axis and 2 units from the x-axis, to the right and above O. Which number is the x-coordinate?
3, the distance from the y-axis.
To move away from the y-axis, you move horizontally, which is the x-direction. So the distance from the y-axis is measured parallel to the x-axis. That distance is what the x-coordinate records.
The x-coordinate of a point is its perpendicular distance from the y-axis, with a sign: positive if the point is to the right of the y-axis, negative if it is to the left.
The y-coordinate is its perpendicular distance from the x-axis, with a sign: positive above the x-axis, negative below.
A point 4 units to the left of the y-axis and 1 unit below the x-axis therefore has x = −4 and y = −1.
The coordinates are written as a pair in brackets, x first: (x, y). Because the order matters, it is called an ordered pair. Formally, P = (3, 2). When labelling a graph, it is usual to write P (3, 2).
Both numbers are always needed. A point in the plane is not “at 3”. It is at (3, 2).
A point on an axis has one coordinate equal to zero.
B (4.5, 0) is on the x-axis, 4.5 units right of O. G (0, −4.5) is on the y-axis, 4.5 units below O. H (0, 4) is on the y-axis, 4 units above O.
📍 Read coordinates off the plane › Drag a point and watch both coordinates change. A brace marks each distance. Move the point onto an axis and one coordinate becomes 0.The definition uses distances, and a distance can be any real number. E (−2.9, 0) is a point on the x-axis, 2.9 units left of O. The unit marks on the axes are for reading positions; a point can lie between them.
1The x-coordinate of a point is its signed perpendicular distance from the…
2A point lies on the x-axis. What must be true of its coordinates?
3The origin is where the axes intersect. Its coordinates are ____.
4Where does each point lie?
5A point is 5 units from the y-axis and 1 unit from the x-axis, to the right and above O. Its coordinates are…
6A point is 4 units left of the y-axis and 1 unit below the x-axis. Its coordinates are…
7Which statement about the Cartesian plane is correct?
Next: the four quadrants, and why the order of the two numbers matters.
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