Ordinate
Key Formula
(x,y)⟹ordinate=y
Where:
- x = The abscissa (x-coordinate), giving the horizontal position
- y = The ordinate (y-coordinate), giving the vertical position
Worked Example
Problem: A point P has coordinates (5, −3). Identify its ordinate and describe what the ordinate tells you about the point's position.
Step 1: Write the point in standard ordered-pair form (x, y).
P=(5,−3)
Step 2: The ordinate is the second value in the ordered pair, which is the y-coordinate.
ordinate=−3
Step 3: Interpret the result: because the ordinate is negative, the point lies 3 units below the x-axis.
Answer: The ordinate of (5, −3) is −3, meaning the point sits 3 units below the x-axis.
Another Example
Problem: Find the ordinate of the point where the line y = 2x + 1 crosses the y-axis.
Step 1: A line crosses the y-axis when x = 0. Substitute x = 0 into the equation.
y=2(0)+1=1
Step 2: The crossing point is (0, 1). The ordinate is the y-coordinate.
ordinate=1
Answer: The ordinate at the y-intercept is 1.
Frequently Asked Questions
What is the difference between ordinate and abscissa?
The abscissa is the x-coordinate (first number in an ordered pair) and measures horizontal distance from the y-axis. The ordinate is the y-coordinate (second number) and measures vertical distance from the x-axis. For the point (4, 7), the abscissa is 4 and the ordinate is 7.
Why is the y-coordinate called the ordinate?
The term comes from the Latin phrase 'linea ordinata applicata,' meaning 'line applied in an orderly manner.' Historically, it referred to a line drawn perpendicular to an axis. Over time, 'ordinate' became shorthand for the vertical coordinate of a point.
Ordinate vs. Abscissa
Both are coordinates of a point (x, y). The abscissa is the first value, x, and gives horizontal position relative to the y-axis. The ordinate is the second value, y, and gives vertical position relative to the x-axis. A simple memory trick: 'Abscissa' and 'Across' both start with A (horizontal), while 'Ordinate' relates to 'Overhead' (vertical).
Why It Matters
The ordinate is essential whenever you read or plot points on the coordinate plane, which underpins graphing, geometry, and data analysis. Many formulas—such as the distance formula, midpoint formula, and slope formula—require you to identify and manipulate y-coordinates separately from x-coordinates. Knowing the precise term also helps when reading older textbooks, standardized tests, and scientific papers that use 'ordinate' instead of 'y-coordinate.'
Common Mistakes
Mistake: Confusing the ordinate with the abscissa and reading the x-coordinate as the ordinate.
Correction: Remember that the ordinate is always the second number in the ordered pair (x, y). It corresponds to the vertical axis. A helpful mnemonic: 'O' for ordinate comes after 'A' for abscissa in the alphabet, just as y comes after x.
Mistake: Treating the ordinate as always positive (ignoring the sign).
Correction: The ordinate can be positive, negative, or zero. A negative ordinate means the point is below the x-axis; zero means it lies exactly on the x-axis.
Related Terms
- Abscissa — The x-coordinate, paired with the ordinate
- Point — A location described by an ordered pair
- Coordinates — The number pair that locates a point
- Coordinate Plane — The grid where ordinate is measured vertically
- Ordered Pair — The (x, y) notation containing the ordinate
- Y-Axis — The vertical axis along which ordinates are scaled
- Y-Intercept — The ordinate where a graph crosses the y-axis