Question

In which quadrants is the abscissa positive?

Short answer

The abscissa is positive in the first and fourth quadrants.

Step-by-step solution

Understand the Coordinate System

The coordinate system is divided into four quadrants by the x-axis (horizontal) and y-axis (vertical). The abscissa refers to the x-coordinate of a point in this system.

Identify Quadrants with Positive Abscissa

The abscissa (x-coordinate) is positive when it is to the right of the y-axis. In the standard coordinate system, this occurs in the first and fourth quadrants.

Conclusion

Therefore, the abscissa is positive in the first and fourth quadrants of the coordinate system.

Key concepts

Understanding the Abscissa

The term abscissa might sound complicated at first, but it's essentially the technical term for what most of us would call the x-coordinate in a coordinate system. Think of the abscissa as the horizontal position of a point—it tells us how far to the right or left the point is from the vertical axis, known as the y-axis.

When you're plotting a point, you'll usually see it written as an ordered pair of numbers like \( (x, y) \). In this pair, the first number is the abscissa. If you see \( (4, 2) \), the abscissa is 4, which means the point is located four units to the right of the y-axis. Conversely, a negative abscissa would indicate a position to the left.

Navigating the Quadrants

The coordinate system is divided into four sections or quadrants, which are helpfully named Quadrant I, Quadrant II, Quadrant III, and Quadrant IV. These quadrants are determined by the intersection of the x-axis and y-axis.

Quadrant I

is in the top right section where both x and y are positive.

Quadrant II

is in the top left, where x is negative, and y is positive.

Quadrant III

is in the bottom left, with both x and y negative. Lastly,

Quadrant IV

is in the bottom right, where x is positive, but y is negative.

To remember which is which, just think 'I' for 'increase'—where both values are getting bigger—and then proceed counterclockwise. Each quadrant has its own unique combination of positive and negative values for the abscissa and the ordinate (which is just another name for the y-coordinate).

When is the Abscissa Positive?

A positive x-coordinate means that we're looking at points that are to the right of the y-axis. If you're facing a graph, it's as if you're standing on the y-axis and looking straight ahead—everything to your right will have a positive x-coordinate.

To identify where the x-coordinate is positive, imagine a vertical line running straight down the center of a page. That's your y-axis. Now, divide the page in half horizontally—that's your x-axis. The right half of the page, which encompasses both the top right and bottom right sections (or Quadrant I and IV), is where your x-coordinate—or abscissa—is positive. Hence, a point with a positive abscissa, such as \( (3, 2) \) or \( (5, -2) \) will always fall into either the first or fourth quadrant.