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. Recall that the rectangular coordinate system is divided into four quadrants, each defined by the signs of the x and y coordinates.
2. Quadrant I contains points where both x and y are positive (x > 0, y > 0).
3. Quadrant II contains points where x is negative and y is positive (x < 0, y > 0).
4. Quadrant III contains points where both x and y are negative (x < 0, y < 0).
5. Quadrant IV contains points where x is positive and y is negative (x > 0, y < 0). Given the point (-1, 3), identify the quadrant by checking the signs of x = -1 and y = 3.

Key Concepts

Rectangular Coordinate System

The rectangular coordinate system, also known as the Cartesian plane, consists of two perpendicular number lines called axes: the x-axis (horizontal) and the y-axis (vertical). Points are located using ordered pairs (x, y), where x indicates horizontal position and y indicates vertical position.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants numbered counterclockwise starting from the upper right. Quadrant I has positive x and y values, Quadrant II has negative x and positive y, Quadrant III has both x and y negative, and Quadrant IV has positive x and negative y.

Determining the Quadrant of a Point

To find the quadrant of a point, examine the signs of its x and y coordinates. For example, a point with x < 0 and y > 0 lies in Quadrant II. This method helps classify points based on their position relative to the axes.