Question

In which quadrants is the ordinate negative?

Short answer

The ordinate is negative in Quadrants III and IV.

Step-by-step solution

Definition of Ordinate

The ordinate in a Cartesian coordinate system refers to the y-coordinate, which indicates the vertical position of a point. A point's ordinate can be positive, negative, or zero.

Understanding the Quadrants

A Cartesian coordinate system is divided into four quadrants by the x-axis and y-axis. The quadrants are numbered counterclockwise starting from the upper right quadrant. In Quadrant I, both x and y are positive. In Quadrant II, x is negative and y is positive. In Quadrant III, both x and y are negative. In Quadrant IV, x is positive and y is negative.

Identifying Negative Ordinate

Based on the signs of the ordinates in each quadrant, we can determine that the ordinates are negative in Quadrants III and IV, where the y-coordinates of points in these quadrants are below the x-axis.

Key concepts

Quadrants of Cartesian Plane

The Cartesian plane, a fundamental concept in geometry and algebra, is a two-dimensional plane formed by two perpendicular lines that intersect at a central point called the origin. These two lines are known as the x-axis (horizontal) and y-axis (vertical), and they divide the plane into four distinct regions called quadrants. Each quadrant contains an infinite number of points, and every point can be represented by a pair of numbers (x, y) known as coordinates.

The numbering of the quadrants begins from the upper right corner and proceeds counterclockwise with Quadrant I to Quadrant IV. Understanding which quadrant a point falls into is crucial as each quadrant defines the sign of the x and y coordinates of that point. This classification aids in graphing equations, solving geometry problems, and interpreting data in a visual format.

Signs of Coordinates

The signs of the coordinates are essential in pinpointing the exact location of a point on the Cartesian plane. Let's delve into what the signs signify in relation to the quadrants:

• In Quadrant I, both coordinates (x, y) are positive, meaning the point lies to the right of the y-axis and above the x-axis.
• In Quadrant II, the x-coordinate is negative and the y-coordinate is positive. Thus, a point here is to the left of the y-axis but still above the x-axis.
• Move to Quadrant III, and you'll find both coordinates are negative. Points here fall to the left of the y-axis and below the x-axis.
• Lastly, in Quadrant IV, while the x-coordinate is positive, the y-coordinate is negative, placing the point to the right of the y-axis but below the x-axis.

By knowing the signs of coordinates, interpreting and plotting points becomes a systematic process, providing clear visual comprehension of geometrical shapes and algebraic equations on the plane.

Quadrants with Negative Ordinates

Focusing on the ordinate, which is another term for the y-coordinate, we identify its role in understanding the position of points with negative ordinates. These belong exclusively to Quadrants III and IV:

• In Quadrant III, as both coordinates are negative, any point here will have a negative ordinate, indicating it's located below the x-axis.
• Similarly, in Quadrant IV, despite the x-coordinate being positive, the ordinate is negative. Points in this quadrant also fall below the x-axis.

Therefore, when assessing where the ordinate is negative, one can immediately look at the positions below the x-axis. This insight is particularly useful when solving equations or graphing functions that require a clear distinction between positive and negative values of y.