Problem 98 - Introductory Algebra for College Students

Question

Explain how to find the coordinates of a point in the rectangular coordinate system.

Step-by-Step Solution

Answer

The coordinates of a point in the Cartesian coordinate system are identified as (x, y), where 'x' represents the distance from the y-axis and 'y' represents the distance from the x-axis. The x-coordinate can be a negative number if the point is to the left of the y-axis and the y-coordinate can be negative if the point is below the x-axis. It is important to remember that the x-coordinate always comes before the y-coordinate.

Step 1: Understand the Layout of the Cartesian Coordinate System

In the Cartesian coordinate system, each point is determined by its position relative to the x-axis (horizontal line) and y-axis (vertical line). The x-axis and y-axis intersect at a point labeled as the origin, denoted by (0,0). When a point is placed in this system, it creates a right-angled triangle with the axes, with the point itself being the triangle's hypotenuse.

Step 2: Identify the x-coordinate

The x-coordinate of a point is the distance from the vertical y-axis to that point. This can either be to the left, denoted by negative numbers, or to the right, denoted by positive numbers.

Step 3: Identify the y-coordinate

The y-coordinate of a point is the distance from the horizontal x-axis to that point. This can be above the x-axis, denoted by positive numbers, or below, denoted by negative numbers.

Step 4: Write the coordinates

The coordinates of a point are commonly written in the format (x, y), where 'x' represents the distance from the y-axis and 'y' represents the distance from the x-axis. The order is important; the x-coordinate always comes before the y-coordinate.