Question

Plot the ordered pairs in a coordinate plane. $$(2,3),(-2,-3),(4,-2)$$

Short answer

To plot the ordered pairs, mark the points (2,3) in the first quadrant, (-2,-3) in the third quadrant, and (4,-2) in the fourth quadrant on a Cartesian plane.

Step-by-step solution

Understand the Cartesian Coordinate System

In a Cartesian coordinate system, points are defined by two coordinates (x, y). The x-coordinate represents the horizontal distance from the origin while the y-coordinate represents the vertical distance. The origin, where both coordinates are zero, is at the center of the grid. The coordinate plane is divided into four quadrants, labeled counterclockwise from top right: the first quadrant (x>0, y>0), second quadrant (x<0, y>0), third quadrant (x<0, y<0), and the fourth quadrant (x>0, y<0).

Identify the Coordinates of the Points

The problem provides three points which will be plotted. They are (2,3), (-2,-3), and (4,-2). For each of these points, the first number is the x-coordinate and the second number is the y-coordinate.

Plot the Points

To plot point (2, 3), start at the origin, move 2 units to the right along the x-axis (since x is positive) and 3 units up along the y-axis (since y is positive). So, the point (2, 3) is in the first quadrant. For (-2,-3), move 2 units to the left along the x-axis (since x is negative) and 3 units down along the y-axis (since y is negative), placing this point in the third quadrant. For (4,-2), move 4 units to the right along the x-axis (since x is positive) and 2 units down the y-axis (since y is negative), so this point lies in the fourth quadrant.