Finding the Coordinates of a Point
Each point in the xyplane has two numbers associated with it.
â€¢ The xcoordinate or abscissa tells how far the point lies to the left
right of the yaxis.
â€¢ The ycoordinate or ordinate tells how far the point lies above or
below the xaxis.
The x and ycoordinates are often written as an ordered pair inside
parentheses, like this: (x, y).
The first number always represents the xcoordinate.
The second number always represents the ycoordinate.
Since the order in which the pair of numbers is written is so important,
(x, y) is called an ordered pair.
For example:
The point (3, 4) has xcoordinate 3 and ycoordinate 4.
This point is located 3 units to the left of the yaxis and 4 units
above the xaxis.
The point (4, 3) has xcoordinate 4 and ycoordinate 3.
This point is located 4 units to the right of the yaxis and 3 units
below the xaxis.
To find the coordinates of a point, we note its location relative to the
x and yaxes.
Procedure â€”
To Find the Coordinates of a Point on a Cartesian
Coordinate System
Step 1 Draw (or imagine) a vertical line through the point. The line
intersects the xaxis at the xcoordinate.
Step 2 Draw (or imagine) a horizontal line through the point. The
line intersects the yaxis at the ycoordinate.
Step 3 Write the coordinates as an ordered pair: (xcoordinate,
ycoordinate).
Example 1
Find the coordinates of point P.
Solution
Step 1 Draw (or imagine) a vertical line through the point.
This line meets the xaxis at 4. The xcoordinate is 4.
Step 2 Draw (or imagine) a horizontal line through the point.
This line meets the yaxis at 2. The ycoordinate is 2.
Step 3 Write the coordinates as an ordered pair.
The coordinates of the point P are (4, 2).
Example 2
Find the coordinates of each labeled point on the graph.
Solution
Point A has coordinates (5, 3).
Point B has coordinates (0, 6).
Point C has coordinates (6, 2).
Point D has coordinates (3, 5).
Point E has coordinates (3, 0).
