Describe the features of a cartesian plane in terms of its axes the direction of axes and its centre

General
1

describe the features of a cartesian plane in terms of its axes the direction of axes and its centre

2

Describe the features of a Cartesian plane in terms of its axes, the direction of axes, and its centre

Answer:
The Cartesian plane, also known as the coordinate plane, is a two-dimensional surface defined by two perpendicular lines called axes. These axes are used to define the coordinates of points in the plane. Here are the features of a Cartesian plane in terms of its axes, the direction of axes, and its center:

1. Axes:

  • X-Axis: This is the horizontal line in the Cartesian plane. It is commonly labeled as the “x-axis” and typically represents the independent variable in functions and data plots.
  • Y-Axis: This is the vertical line in the Cartesian plane. It is labeled as the “y-axis” and usually represents the dependent variable.

2. Direction of Axes:

  • Positive Direction on the X-Axis: On the x-axis, values increase to the right. Moving from the origin (center) to the right is considered the positive direction.
  • Negative Direction on the X-Axis: On the x-axis, values decrease to the left of the origin. Moving from the origin to the left is considered the negative direction.
  • Positive Direction on the Y-Axis: On the y-axis, values increase upwards. Moving from the origin upwards is considered the positive direction.
  • Negative Direction on the Y-Axis: On the y-axis, values decrease downwards. Moving from the origin downwards is considered the negative direction.

3. Centre (Origin):

  • The center of the Cartesian plane is called the origin. It is the point where the x-axis and y-axis intersect.
  • Coordinates of the Origin: The origin has coordinates (0, 0), meaning it is zero units away from both the x-axis and the y-axis.

Special Features:

  • Quadrants: The Cartesian plane is divided into four quadrants:
    1. Quadrant I: Located in the upper right, where both x and y coordinates are positive ((x > 0, y > 0)).
    2. Quadrant II: Located in the upper left, where x coordinates are negative and y coordinates are positive ((x < 0, y > 0)).
    3. Quadrant III: Located in the lower left, where both x and y coordinates are negative ((x < 0, y < 0)).
    4. Quadrant IV: Located in the lower right, where x coordinates are positive and y coordinates are negative ((x > 0, y < 0)).

Visual Representation:

\begin{array}{c|c} & y \text{-axis} \\ \text{Quadrant II} & \text{Quadrant I} \\ \text{(negative, positive)} & \text{(positive, positive)} \\ & \\ \hline \text{Quadrant III} & \text{Quadrant IV} \\ \text{(negative, negative)} & \text{(positive, negative)} \\ \end{array}

In summary, the Cartesian plane consists of two perpendicular axes that intersect at the origin, dividing the plane into four quadrants. The directions along these axes are clearly defined, with positive and negative directions for both the x-axis and y-axis. Understanding these features is crucial for working with coordinates, plotting functions, and analyzing geometric relationships in two dimensions.