How far from each axis?
(x, y): x from the y-axis, y from the x-axis.
Two distances
A point P is 4 units from the y-axis and 3 units from the x-axis. It lies in the top-right part of the plane.
Which number is the x-coordinate of P?
What this lesson covers
The idea
A point P has coordinates (x, y), written P (x, y): the x-coordinate x is its perpendicular distance from the y-axis, and the y-coordinate y is its perpendicular distance from the x-axis.
Two distances
A point P is 4 units from the y-axis and 3 units from the x-axis. It lies in the top-right part of the plane.
Which number is the x-coordinate of P?
- 4
- 3
- Both are the same
Measure from the axes
The dashed lines show how far P is from each axis. Blue is the distance along the x-axis; orange is the distance along the y-axis.
Reading (x, y)
A point P has coordinates (x, y), written P (x, y). The x-coordinate x is its perpendicular distance from the y-axis. The y-coordinate y is its perpendicular distance from the x-axis.
The order matters: the x-number always comes first.
- Point | x-coordinate | y-coordinate
- S (3, −5) | 3 | −5
- Q (−5, 3) | −5 | 3
Notes
The point P (x, y): x is its distance from the y-axis; y is its distance from the x-axis. The order matters.
Check yourself
P is 6 units from the y-axis and 1 unit from the x-axis, in the top-right part. Its coordinates are…
What are the coordinates of point A?
Are (3, 5) and (5, 3) the same point?
What is the y-coordinate of S (3, −5)?
Answer: -5
The second number is the y-coordinate: −5. S is 5 units below the x-axis.
- (6, 1) — correct. Yes. x is the distance from the y-axis (6) and y is the distance from the x-axis (1).
- (1, 6). That swaps the numbers. x is the distance from the y-axis, which is 6.
- (−6, 1). P is in the top-right part, so x is positive.
- (−4, 3) — correct. Yes. A is 4 units left of the y-axis (x = −4) and 3 units above the x-axis (y = 3).
- (4, 3). A is to the left of the y-axis, so x is negative.
- (3, −4). The x-number comes first. A is 4 units left and 3 units up.
- (−4, −3). A is above the x-axis, so y is positive.
- Yes, they use the same numbers. The order matters. (3, 5) is 3 from the y-axis and 5 from the x-axis. (5, 3) is the other way round.
- No, they are different points — correct. Right. If x ≠ y, then (x, y) ≠ (y, x).