Question

Which quadrant has negative \(x\) values and negative \(y\) values? A. Ql B. Qll C. QIII D. QIV

Short answer

C. QIII

Step-by-step solution

Understand the Cartesian Plane

The Cartesian plane is divided into four quadrants. Each quadrant is defined by the signs of the x and y coordinates.

Analyze the Signs

In Quadrant I (QI), both x and y are positive. In Quadrant II (QII), x is negative and y is positive. In Quadrant III (QIII), both x and y are negative. In Quadrant IV (QIV), x is positive and y is negative.

Identify the Correct Quadrant

Since the problem requires both x and y to be negative, this corresponds to Quadrant III (QIII).

Key concepts

negative coordinates

Understanding negative coordinates is crucial when working with the Cartesian plane. Coordinates are pairs of values, noted as \((x, y)\), which determine a point's position on the plane.
Negative coordinates indicate that the point is located to the left of the y-axis (for negative x-values) or below the x-axis (for negative y-values).
When both coordinates \((x, y)\) are negative, the point falls in the lower-left section of the Cartesian plane.

quadrant analysis

Performing a quadrant analysis helps us to identify in which section of the Cartesian plane a point belongs. The plane is divided into four quadrants:

• Quadrant I (QI): both x and y are positive \((+, +)\)
• Quadrant II (QII): x is negative and y is positive \((- , +)\)
• Quadrant III (QIII): both x and y are negative \((- , -)\)
• Quadrant IV (QIV): x is positive and y is negative \((+, -)\)

By examining the signs of the coordinates, we can determine which quadrant a point is located in.

quadrant III

Quadrant III is a vital concept for learning about negative coordinate values in the Cartesian plane. It is located in the lower-left section of the plane.
In this quadrant, both the x-coordinate and the y-coordinate are negative \((- , -)\).
Therefore, any point located in Quadrant III will be positioned to the left of the y-axis and below the x-axis.
Understanding this helps in identifying and solving problems involving negative coordinates.