In the following exercises, plot each point in a rectangular...

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.
(a) (-4,2)
(b) (-1,-2)
(c) (3,-5)
(d) (-3,5)
(e) $\left(\frac{5}{3}, 2\right)$

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Key Concepts

Plotting Points

Plotting points involves marking locations on the Cartesian plane using their coordinate pairs. This process is essential for visually representing mathematical data and understanding the spatial relationships between different points, which is a fundamental skill in coordinate geometry.

Quadrants

The Cartesian plane is divided into four quadrants, each determined by the sign of the x and y coordinates. The first quadrant has both coordinates positive, the second has a negative x and positive y, the third has both negative, and the fourth has a positive x and negative y. Understanding the quadrants aids in identifying where a specific point lies based on the signs of its coordinates.

Cartesian Coordinate System

The Cartesian coordinate system is a two-dimensional plane defined by two perpendicular axes: the horizontal x-axis and the vertical y-axis. It serves as the foundation for plotting points, lines, and other figures, allowing for a systematic way to describe the position of any point in the plane using pairs of numbers.

Coordinate Pair

A coordinate pair, typically written as (x, y), represents the position of a point in the Cartesian coordinate system. The first number indicates the location along the x-axis (horizontal position), while the second number indicates the position along the y-axis (vertical position).

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