Fill in the blank to correctly complete each sentence. The point (-1, 3) lies in quadrant ________ in the rectangular coordinate system.

Verified step by step guidance

1. Identify the coordinates of the point (-1, 3).
2. Recall that the rectangular coordinate system is divided into four quadrants.
3. Understand that the x-coordinate is negative and the y-coordinate is positive.
4. Recognize that points with a negative x-coordinate and a positive y-coordinate lie in Quadrant II.
5. Conclude that the point (-1, 3) lies in Quadrant II.

Key Concepts

Quadrants in the Coordinate System

The rectangular coordinate system, also known as the Cartesian plane, is divided into four quadrants. Quadrant I is where both x and y coordinates are positive, Quadrant II has a negative x and positive y, Quadrant III has both coordinates negative, and Quadrant IV has a positive x and negative y. Understanding these quadrants is essential for determining the location of points based on their coordinates.

Coordinate Points

A coordinate point is represented as an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position on the Cartesian plane. The sign of each coordinate determines the quadrant in which the point lies. For example, a point with a negative x and a positive y, like (-1, 3), will be located in Quadrant II.

Sign of Coordinates

The sign of the coordinates (positive or negative) is crucial for identifying the quadrant of a point in the Cartesian plane. A positive x-coordinate indicates a position to the right of the origin, while a negative x-coordinate indicates a position to the left. Similarly, a positive y-coordinate indicates a position above the origin, and a negative y-coordinate indicates a position below it, helping to classify the point's location.