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91Ó°ÊÓ

Plot each point on a rectangular coordinate system and name the quadrant or axis in which the point lies. $$ (-2,1) $$

Short Answer

Expert verified
The point (-2,1) is in Quadrant II.

Step by step solution

01

Understanding the Coordinate System

The rectangular coordinate system, also known as the Cartesian coordinate system, consists of two perpendicular axes: the horizontal x-axis and the vertical y-axis. The point (-2,1) has an x-coordinate of -2 and a y-coordinate of 1.
02

Plotting the Point

To plot the point (-2,1), start by moving horizontally along the x-axis to x = -2. From there, move vertically to y = 1. Mark this location on the graph.
03

Identifying the Quadrant or Axis

Quadrants are defined as: - Quadrant I: (+x, +y) - Quadrant II: (-x, +y) - Quadrant III: (-x, -y) - Quadrant IV: (+x, -y) The point (-2, 1) lies in Quadrant II, where x is negative and y is positive.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

plotting points
Plotting points on the Cartesian coordinate system is a key foundational skill in understanding graphing. It involves identifying the specific location of a point on a graph defined by its x and y coordinates. The x-coordinate tells you how far to move horizontally from the origin, and the y-coordinate tells you how far to move vertically. Here’s how to do it:
  • Start at the origin, where the x-axis and y-axis intersect. This is the point (0,0).
  • The x-coordinate comes first. If it’s negative, move left; if positive, move right. For example, for the point (-2,1), move two units to the left.
  • The y-coordinate follows. If it’s positive, move up; if negative, move down. For the point (-2,1), move one unit up.
  • The place where you stop is the point (-2,1). Mark it clearly on the graph.
With practice, you will plot these points intuitively.
quadrants
Quadrants are the four sections of the Cartesian coordinate system, divided by the x and y axes. They help in identifying the specific area where the point lies based on its x and y values. The quadrants are ordered counter-clockwise starting from the upper right, where both x and y are positive. Here's a quick overview:
  • Quadrant I: Here, both x and y coordinates are positive (+x, +y).
  • Quadrant II: In this quadrant, x is negative while y is positive (-x, +y). The point (-2,1) falls here.
  • Quadrant III: Both coordinates are negative here (-x, -y).
  • Quadrant IV: Here, x is positive, and y is negative (+x, -y).
The axes that divide these quadrants are not part of any quadrant but rather define them.
Cartesian coordinate system
The Cartesian coordinate system is a mathematical 2D number line grid, where points are identified using pairs of numerical coordinates. These axes are perpendicular, creating a graph with a wide variety of possible numbers of coordinates. In this graph:
  • The x-axis represents horizontal movement.
  • The y-axis represents vertical movement.
The point where the x-axis and y-axis meet is known as the origin, marked as (0,0). On this grid, each point can be found using ordered pairs (x, y), where the x-value shows the horizontal position relative to the origin, and the y-value shows the vertical position. This system, named after René Descartes, creates a structured way to depict geographic, statistical, or any numerical data, offering a visual understanding of values and their relationships in mathematics.

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