Plot the given point in a rectangular coordinate system. (1, 4)

Verified step by step guidance

1. Understand the rectangular coordinate system: It consists of two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical), which intersect at the origin (0, 0). Points are represented as ordered pairs (x, y).
2. Identify the given point: The point (1, 4) consists of an x-coordinate of 1 and a y-coordinate of 4.
3. Locate the x-coordinate: Start at the origin (0, 0) and move 1 unit to the right along the x-axis, since the x-coordinate is positive.
4. Locate the y-coordinate: From the position at x = 1, move 4 units upward along the y-axis, since the y-coordinate is positive.
5. Mark the point: Place a dot at the location corresponding to (1, 4) and label it appropriately on the rectangular coordinate system.

Key Concepts

Rectangular Coordinate System

A rectangular coordinate system, also known as the Cartesian coordinate system, consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point in this system is defined by an ordered pair (x, y), where 'x' represents the horizontal position and 'y' represents the vertical position. This framework allows for the precise plotting of points and the visualization of geometric relationships.

Ordered Pairs

An ordered pair is a pair of numbers used to represent a point in a coordinate system. The first number indicates the position along the x-axis, while the second number indicates the position along the y-axis. For example, the ordered pair (1, 4) means the point is located 1 unit to the right of the origin on the x-axis and 4 units up on the y-axis, providing a clear method for locating points in a two-dimensional space.

Plotting Points

Plotting points involves marking a specific location on a coordinate grid based on its ordered pair. To plot the point (1, 4), one would start at the origin (0, 0), move 1 unit to the right along the x-axis, and then move 4 units up along the y-axis. This process is fundamental in graphing functions, analyzing relationships, and visualizing data in mathematics.