What is the Cartesian Coordinate System? | Don't Memorise

Summary

This video explains the basics of the Cartesian coordinate system, introducing the concept of plotting points on a graph. The x-axis and y-axis are defined, with positive and negative numbers marked on both axes. The origin is explained as the reference point where the two axes meet. A point's location is described using coordinates, such as (3, 2), where the first number is the x-coordinate and the second is the y-coordinate. The importance of the order of coordinates is emphasized, and the video sets the stage for further learning about the Cartesian plane.

Takeaways

• 😀 The x and y axes are drawn and labeled as 'x-x' and 'y-y' respectively.
• 😀 The axes are numbered, with positive integers (1, 2, 3, etc.) on both the x-axis and y-axis in the positive direction.
• 😀 Negative numbers are marked on the left side of the x-axis and the lower side of the y-axis (e.g., -1, -2, -3, etc.).
• 😀 The reference point or origin is zero, located at the intersection of the x and y axes.
• 😀 All intervals on the axes are marked in equal increments, ensuring uniformity across the plane.
• 😀 Points on the plane are denoted using coordinates (x, y), where 'x' is the distance from the origin along the x-axis, and 'y' is the distance from the origin along the y-axis.
• 😀 A random point P is shown to be 3 units away from the origin on the x-axis and 2 units on the y-axis, represented as (3, 2).
• 😀 The coordinates (3, 2) are an ordered pair, with the x-coordinate always written first and the y-coordinate second.
• 😀 The order of the coordinates is important—(2, 3) is a different point from (3, 2).
• 😀 This system of denoting points using ordered pairs is called the Cartesian coordinate system, which is fundamental in mathematics.

Q & A

What is the Cartesian coordinate system?

The Cartesian coordinate system is a method used to locate points on a plane using two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Points are identified by their coordinates, written as an ordered pair (x, y), where 'x' is the distance from the y-axis and 'y' is the distance from the x-axis.

Why are the x and y coordinates written in a specific order?

The order of the coordinates matters because the first value refers to the horizontal position (x-axis), and the second value refers to the vertical position (y-axis). Reversing them would result in a different point on the graph.

How do we represent negative numbers on the axes?

Negative numbers are marked on both axes in equal intervals. On the x-axis, negative numbers like -1, -2, -3, etc., are placed to the left of the origin (0), while on the y-axis, negative numbers like -1, -2, -3, etc., are placed below the origin.

What is the significance of the origin in the Cartesian coordinate system?

The origin, denoted as (0, 0), is the reference point in the Cartesian coordinate system where both the x-axis and y-axis intersect. It serves as the starting point for measuring distances along both axes.

What is the meaning of an ordered pair in the Cartesian coordinate system?

An ordered pair represents the location of a point on the coordinate plane. It consists of two values: the x-coordinate (horizontal position) and the y-coordinate (vertical position). The order in which these values are written is crucial as it determines the correct position of the point.

How do we write the coordinates of a point located 3 units on the x-axis and 2 units on the y-axis?

The coordinates of a point located 3 units on the x-axis and 2 units on the y-axis are written as (3, 2). This means the point is 3 units to the right of the origin along the x-axis and 2 units up along the y-axis.

What happens if the coordinates are written as (2, 3) instead of (3, 2)?

Writing the coordinates as (2, 3) would refer to a different point. The point (2, 3) is located 2 units to the right on the x-axis and 3 units up on the y-axis, while (3, 2) would be 3 units to the right on the x-axis and only 2 units up on the y-axis.

What does it mean for the Cartesian coordinate system to have 'equal intervals'?

The phrase 'equal intervals' means that the distance between each number on the axes is the same. Whether on the positive or negative side of the axis, the intervals are evenly spaced, ensuring consistency in plotting points.

What is the importance of the origin being at (0, 0) on the axes?

The origin being at (0, 0) provides a consistent reference point for all other points on the graph. This makes it possible to precisely measure distances and define the location of any point on the plane in relation to the origin.

How does the Cartesian coordinate system help in mathematical analysis?

The Cartesian coordinate system allows for precise representation and analysis of geometric shapes, functions, and relationships. By plotting points and curves on the plane, it provides a visual and algebraic tool for studying mathematical problems.