Understanding Coordinate Quadrants and Negative Values

The question asks us to identify the specific quadrant in the Cartesian coordinate system where both the abscissa (which is the x-coordinate) and the ordinate (which is the y-coordinate) have negative values.

Defining Abscissa and Ordinate

In a coordinate plane:

• The abscissa refers to the horizontal position of a point, represented by the x-coordinate.
• The ordinate refers to the vertical position of a point, represented by the y-coordinate.

Exploring the Cartesian Quadrants

The Cartesian plane is divided into four quadrants by the x-axis (horizontal) and the y-axis (vertical).

• Quadrant I: Located in the top-right, both abscissa (x) and ordinate (y) are positive. (x > 0, y > 0)
• Quadrant II: Located in the top-left, the abscissa (x) is negative, and the ordinate (y) is positive. (x < 0, y > 0)
• Quadrant III: Located in the bottom-left, both the abscissa (x) and the ordinate (y) are negative. (x < 0, y < 0)
• Quadrant IV: Located in the bottom-right, the abscissa (x) is positive, and the ordinate (y) is negative. (x > 0, y < 0)

Identifying the Quadrant with Negative Coordinates

We are looking for the quadrant where both the abscissa and the ordinate are negative. Based on the definitions above:

• Quadrant I has positive values for both.
• Quadrant II has a negative abscissa and a positive ordinate.
• Quadrant III has a negative abscissa and a negative ordinate.
• Quadrant IV has a positive abscissa and a negative ordinate.

Therefore, the quadrant where both the abscissa and the ordinate are negative is the Third quadrant.

This confirms that the Third quadrant is the correct location for points with negative abscissa and negative ordinate values.