CONCEPT PREVIEW Fill in the blank(s) 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). Since the point (-1, 3) has x = -1 (negative) and y = 3 (positive), it lies in Quadrant II.

Key Concepts

Rectangular Coordinate System

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

Quadrants in the Coordinate Plane

The coordinate plane is divided into four quadrants numbered counterclockwise starting from the upper right: Quadrant I (+x, +y), Quadrant II (-x, +y), Quadrant III (-x, -y), and Quadrant IV (+x, -y). The sign of the coordinates determines the quadrant location.

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 a negative x and positive y coordinate lies in Quadrant II. This method helps classify points based on their position relative to the axes.