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# Finding the Coordinates of a Point

Each point in the xy-plane has two numbers associated with it.

â€¢ The x-coordinate or abscissa tells how far the point lies to the left right of the y-axis.

â€¢ 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 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 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).