What Is y-Coordinate?
The y-coordinate tells you how far up or down the point lies in relation to the origin. It is the second element of the ordered pair (x, y). It defined the perpendicular distance of the point from the X-axis.
The y-coordinate is also called the “ordinate.”
The x-coordinate is also called the “abscissa.”
In the Cartesian coordinate plane, the x-coordinate and y-coordinate represent the positions of points in two-dimensional space.
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What Is an Ordered Pair?
On the 2D plane or the XY plane, each point has two coordinates, x-value and y-value, which help us locate the point easily. It is represented using an ordered pair (x, y). The x-coordinate refers to a horizontal position along the x-axis, while the y-coordinate refers to a vertical position along the y-axis.
In the ordered pair (x, y), the first element x is the perpendicular distance of the point from the y-axis and the second element y is the perpendicular distance of the point from the x-axis.
What Is the Cartesian Coordinate System?
The X-axis and Y-axis are two perpendicular lines creating the two-dimensional Cartesian coordinate system. The point where the two axes meet is called the origin (0,0). Together, the x-axis and y-axis allow you to locate points in two-dimensional space by specifying their x-coordinate (horizontal position) and y-coordinate (vertical position).
- X-axis: The X-axis is the horizontal line in the Cartesian coordinate system. It runs from left to right, and it is used to represent the horizontal position of points. The X-axis is labeled with numbers that increase as you move to the right and decrease as you move to the left.
The equation of the X-axis is given by y = 0 since the y-coordinate of any point on the X-axis is always 0. - Y-axis: The Y-axis is the vertical line in the Cartesian coordinate system. It runs from bottom to top, and it represents the vertical position of points. The y-axis is labeled with numbers that increase as you move upward and decrease as you move downward.
The equation of the Y-axis is x = 0 since the x-coordinate of any point on the Y-axis is always 0.
Definition of y-Coordinate
The y-coordinate is a value that represents a point’s vertical position on a graph. The y-coordinate of a point is the second element in the ordered pair (x, y).
What Does the y-Coordinate of a Point Tell You?
The y-coordinate is a value that represents the vertical position of a point in a two-dimensional Cartesian coordinate system. It specifies the distance of a point from the horizontal axis, known as the x-axis.
The y-coordinate indicates the vertical location of a point along the y-axis. If the y-coordinate is positive, the point is above the x-axis; if it’s negative, the point is below.
The x-coordinate, in contrast, is a horizontal coordinate that allows you to see where you are on the graph.
Example: In the given graph, the point (4, 2) is plotted.
The x-coordinate is 4. The y-coordinate is 2.
Notice that the point (4, 2) is exactly 4 units right with respect to the origin. Thus, the x-coordinate is 4.
It is 2 units up from the origin, since the y-coordinate is 2. It defines the vertical position of the point.
Sign Convention of y-Coordinate in the Four Quadrants
In a 2D plane, the origin is the point of intersection of the two axes. At the origin, the value of both x-coordinate and y-coordinate is zero.
(1) The value of the y-coordinate of a point lying above the x-axis or above the origin will always be positive. Similarly, the value of the y-coordinate of a point lying below the x-axis and the origin will always be negative.
(2) The value of the x-coordinate on the right side of the y-axis will always be positive. Similarly, the value of the X-coordinate on the left side of the y-axis will always be negative.
How to Plot the y-Coordinate on a Graph
Y-coordinates are represented with graphs by placing them on either axis at an intersection that represents their value. The Y-axis is found on every graph to represent vertical position or displacement.
- In the first quadrant, the y-coordinate is always positive. It is because the first quadrant is defined by the positive X-axis and positive Y-axis.
- In the second quadrant, the y-coordinate is always positive. It is because the second quadrant is defined by the negative X-axis and positive Y-axis.
- In the third quadrant, the y-coordinate is always negative. It is because the third quadrant is defined by the negative X-axis and negative Y-axis.
- In the fourth quadrant, the y-coordinate is always negative. It is because the fourth quadrant is defined by the positive X-axis and negative Y-axis.
- On the X-axis, the y-coordinate is always 0.
Example 1: The y-coordinate of the point (3, 3) is 3.
Examples:
i) A (3, 4)
3 is the x-coordinate, and 4 is the y-coordinate. This is because A is 3 units away from the y-axis. It is 4 units away from the x-axis.
ii) B (-4, 0)
-4 is the x-coordinate. 0 is the y-coordinate. The point B is 4 units towards the left from the origin the X-axis, its value is negative, and because it didn’t move vertically along the y-axis, its value is 0.
iii) C (4, -4)
The point lies 4 units down from the X-axis. Thus, the vertical distance is defined by the y-coordinate -4.
The point is 4 units to the right from the Y-axis. Thus, the horizontal distance is defined by the x-coordinate 4.
How to Find the y-Coordinate of a Given Point
i) In the ordered pair (a, b), the y-coordinate is the second element, b.
For example, the y-coordinate of (1, 3) is 3.
ii) On a graph, the y-coordinate of the point tells you the vertical position of the point. You can just trace back the point using a line to its corresponding point in the Y-axis. The corresponding parallel coordinate on the Y-axis is the required coordinate.
Example: Consider a point plotted on a graph.
The corresponding point on the X-axis is (2, 0). Thus, the x-coordinate is 2. It tells us that the point is 2 units to the right of the Y-axis, defining the horizontal position.
The corresponding point on the Y-axis is (0, 4). Thus, the y-coordinate is 4. It tells us that the point lies 4 units up from the X-axis, defining the vertical position.
As shown in the picture above, the coordinates for the given point are (2,4).
Facts about the y-coordinate
- If the y-coordinate of a point is 0, then the point lies on the X-axis.
- Both the x-coordinate and y-coordinate of the origin are 0, since it lies on the intersection of both the axes.
- Cartesian coordinates of a point are also called rectangular coordinates since plotting a point resembles the shape of a rectangle.
Conclusion
In this article, we learned about the y-coordinate of a point, its definition, and its interpretation on a graph. Let’s solve a few examples and practice MCQs for better comprehension.
Solved Examples on the y-coordinate
1. Find the value of the y-coordinate of point A in the given graph:
Solution:
The y-coordinate is always located along the y-axis. It represents the vertical distance.
The point is located 5 units above the x-axis, which means its value will be positive.
So, the y-coordinate of the will be +5, or just 5.
2. The coordinates of the point are (2,4). Find the quadrant in which the point lies.
Solution:
The coordinates of the point are (2,4). Both the coordinates are positive. As both the coordinates are positive, the point is located in the first quadrant.
Let’s plot the point to understand this better.
3. Find the x and y-coordinates of the given point on the graph.
Solution:
The point in the above graph is the origin. It is the intersection point of the X-axis and the Y-axis.
Its coordinates are (0,0).
4. Starting from the center of the classroom (origin), Jack first walked 3 units to the right. Next, he walked 7 units up. Find the y-coordinate of his position.
Solution:
Jack walked 3 feet horizontal distance and 7 feet vertical distance.
Thus, the y-coordinate of his current position is 7.
Practice Problems on the y-coordinate
Y Coordinate - Definition, Facts, Examples, FAQs, How to Find
In the given image, find the y-coordinate of the given point:
The point is located 2 units above the x-axis.
Thus, the coordinate of the point is +2.
The y-coordinates of three points A, B, and C, are (3,2), (− 3, 4), and (− 2, −5), respectively. Find out in which quadrant these points are located.
(3,2): (+,+): First quadrant
(− 3, 4): (−, +): Second quadrant
Third quadrant: (− , −): Third quadrant
The given image shows how John walked on a field starting from the center. What is the y-coordinate of his current position?
Horizontal distance covered along the +ve X-axis = 5 yards
Vertical distance covered along the +ve Y-axis = 6 yards
Thus, the y-coordinate is 6.
Frequently Asked Questions about the y-coordinate
What does the y-coordinate tell you?
The y-value tells us how far along a point lies in the y-direction or vertical direction.
What is the y-intercept?
The y-intercept of a line is the point on the graph where the line crosses the y-axis. It is the value of y when x = 0.
When is the y-coordinate negative?
The y-coordinate of a point is negative when the point lies below the origin.
