Finding the Coordinates of a Point
Each point in the xy-plane has two numbers associated with it.
• The x-coordinate or abscissa tells how far the point lies to the left
right of the y-axis.
• The y-coordinate or ordinate tells how far the point lies above or
below the x-axis.
The x- and y-coordinates are often written as an ordered pair inside
parentheses, like this: (x, y).
The first number always represents the x-coordinate.
The second number always represents the y-coordinate.
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 x-coordinate -3 and y-coordinate 4.
This point is located 3 units to the left of the y-axis and 4 units
above the x-axis.
The point (4, -3) has x-coordinate 4 and y-coordinate -3.
This point is located 4 units to the right of the y-axis and 3 units
below the x-axis.
To find the coordinates of a point, we note its location relative to the
x- and y-axes.
Procedure —
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 x-axis at the x-coordinate.
Step 2 Draw (or imagine) a horizontal line through the point. The
line intersects the y-axis at the y-coordinate.
Step 3 Write the coordinates as an ordered pair: (x-coordinate,
y-coordinate).
Example 1
Find the coordinates of point P.
Solution
Step 1 Draw (or imagine) a vertical line through the point.
This line meets the x-axis at -4. The x-coordinate is -4.
Step 2 Draw (or imagine) a horizontal line through the point.
This line meets the y-axis at 2. The y-coordinate 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).
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