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X and Y Coordinates

X and Y Coordinates help in identifying a point in the coordinate axes and are written as the ordered pair (x, y). The coordinates of a point are referred as (x, y), where x represents the position of the point with reference to the x-axis, and y represents the position of the point with reference to the y-axis.

Let us learn more about x and y coordinates, their location, and their uses.

1. What Are X and Y Coordintes?
2. X and Y Coordinates in Four Quadrants
3. How to Find X and Y Coordinates?
4. Uses of X and Y Coordinates
5. Examples on X and Y Coordinates
6. Practice Questions
7. FAQs on X and Y Coordinates

What Are X and Y Coordinates?

X and Y coordinates is an address, which helps to locate a point in two-dimensional space. Any point in the coordinate plane is referred by a point (x, y), where the x value is the position of the point with reference to the x-axis, and the y value is the position of the point with reference to the y-axis. The x and y coordinates of a point have positive or negative values, based on the location of the point in the different quadrants.

Here let us look at these two important terms relating to x and y coordinates.

  • Abscissa (x coordinate): It is the x value in the point (x, y), and is the length of the perpendicular drawn from the point to the y-axis. i.e., it is the horizontal distance from the point to the y-axis.
  • Ordinate (y-coordinate) : It is the y value in the point (x, y)., and is the length of the perpendicular drawn from the point to the x-axis. i.e., it is the vertical distance from the point to the x-axis.

X and Y Coordinates In Four Quadrants

The properties of the x and y coordinates of a point represented in the four quadrants of the cartesian plane are as follows.:

  • The x and y coordinates of the origin is equal to (0, 0), which is the point of intersection of the x-axis and y-axis.
  • The x and y coordinates of a point on the x-axis is of the form (a, 0), and here the y coordinate of the point is equal to zero.
  • The x and y coordinates of a point on the y-axis is of the form (0, b) and here the x coordinate of the point is equal to zero.
  • The point represented in the first quadrant (x, y) has both positive values and is plotted with reference to the positive x-axis and the positive y-axis.
  • The point represented in the second quadrant is (-x, y) and is plotted with reference to the negative x-axis and positive y-axis.
  • The point represented in the third quadrant (-x, -y) is plotted with reference to the negative x-axis and negative y-axis.
  • The point represented in the fourth quadrant (x, -y) is plotted with reference to the positive x-axis and negative y-axis.

X and Y Coordinates in Four Quadrantts

How to Find X and Y Coordinates?

To find the x and y coordinates of a given point,

  • See what is its perpendicular distance from the y-axis and it is your x-coordinate (x).
  • See what is its perpendicular distance from the x-axis and it is your y-coordinate (y).
  • Write the x and y values in the ordered pair (x, y) and change the signs of x and y according to the quadrant that it lies in.

Example: Find the x and y coordinates of the point A shown.

How to Find X and Y Coordinates

Solution:

Draw horizontal and vertical lines from point A to the y and x-axes respectively and see what they measure.

writing x and y coordinates

Now, keeping in mind that point A lies in quadrant 4, A = (2, -5).

Uses of X and Y Coordinates

The x and y coordinates of a point are useful to perform numerous operations of finding distance, midpoint, the slope of a line, equation of a line, etc. Further, some of the other important uses of the x and y coordinates of a point are as follows.

  • The x and y coordinates help in locating a point on the coordinate axes.
  • The x and y coordinates for two given points can be used to find the distance between the two points.
  • The x and y coordinates for two points help in finding the slope of a line.
  • The x and y coordinates for two points help in finding the equation of a line.

☛ Related Topics:

 

Examples on X and Y Coordinates

  1. Example 1: Find the x and y coordinates of the midpoint of the line joining the points (5, -3), (1, 7).

    Solution:

    The given points are (x1, y1) = (5, -3), and (x2, y2) = (1, 7).

    The midpoint of the line connecting these points is M.P = ((x1 + x2)/2, (y1 + y2)/2)

    = ((5 + 1) / /2, (-3 + 7) / 2)

    = (6/2, 4/2)

    = (3, 2)

    Answer: Therefore, the x and y coordinates of the midpoint of the line joining the two points is (3, 2).

  2. Example 2: What is the x and y coordinates of the centroid of the triangle having its vertices as (2, 0), (5, 2), (-1, 4)?

    Solution:

    The three vertices of the triangle are (x1, y1) = (2, 0), (x2, y2) = (5, 2), (x3, y3) = (-1, 4).

    The coordinates of the centroid of the triangle is C = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

    = ((2 + 5 + (-1))/3, (0 + 2 + 4)/3)

    = (6/3, 6/3)

    = (2, 2)

    Answer: Therefore, the x and y coordinates of the centroid of the triangle is (2, 2).

  3. Example 3: If |x| = 3 and |y| = 4 and the point (x, y) is in quadrant II, then what are the x and y coordinates?

    Solution:

    The absolute values of x and y are given as follows:

    |x| = 3 ⇒ x = ± 3

    |y| = 4 ⇒ y = ± 4

    Since (x, y) is in quadrant II, x is negative and y is positive. Therefore, x = -3 and y = 4.

    Answer: The x and y coordinates ate -3 and 4 respectively.

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FAQs on X and Y Coordinates

How Do You Identify X and Y Coordinates?

The x and y coordinates can be easily identified from the given point in the coordinate axes. For a point (a, b), the first value is always the x coordinate, and the second value is always the y coordinate.

How Do You Write the X and Y Coordinates?

The x and y coordinates are written as (x, y). Here the x and y values can have positive or negative values. The x value of the point is called abscissa, and the y value of the point is called ordinate.

Which is First X or Y Coordinate?

We always write the x-coordinate first and then the y-coordinate. We write as (x, y) and we call it an "ordered pair" as there is importance for the order.

What Is the X and Y Coordinates In The Four Quadrants?

The values of x and y coordinates of a point in the four quadrants can be understood from the below points.

  • If (x, y) is in quadrant 1 then x > 0 and y > 0.
  • If (x, y) is in quadrant 2 then x < 0 and y > 0.
  • If (x, y) is in quadrant 3 then x < 0 and y < 0.
  • If (x, y) is in quadrant 4 then x > 0 and y < 0.

What Are the X and Y Coordinates Of The Origin?

The x and y coordintes of the origin is (0, 0). It is usually represented with the letter 'O'.

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