CARTESIAN COORDINATE SYSTEM || GRADE 8 MATHEMATICS Q1

Summary

This video introduces the Cartesian coordinate system, covering its definition, components such as the x-axis, y-axis, quadrants, and the origin. It explains how this two-dimensional system allows movement in both horizontal and vertical directions, contrasting it with the one-dimensional number line. The presenter discusses the historical context of the system, attributed to René Descartes, and details how to plot points based on ordered pairs. Additionally, viewers learn about the signs of coordinates in different quadrants and how to determine the quadrant for given points, enhancing their understanding of this fundamental mathematical concept.

Takeaways

• 😀 The Cartesian coordinate system consists of two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical).
• 😀 The origin is the point where the x-axis and y-axis intersect, and its coordinates are (0, 0).
• 😀 The Cartesian plane is a two-dimensional coordinate system used for graphing ordered pairs.
• 😀 Quadrants are formed by the intersection of the axes and are labeled counterclockwise as Quadrant I, II, III, and IV.
• 😀 In Quadrant I, both x and y coordinates are positive, while in Quadrant II, x is negative and y is positive.
• 😀 Quadrant III has both x and y coordinates as negative, and Quadrant IV has a positive x coordinate and a negative y coordinate.
• 😀 The x-coordinate is also known as the abscissa, and the y-coordinate is referred to as the ordinate.
• 😀 When plotting points on the Cartesian plane, always start from the origin and move according to the signs of the coordinates.
• 😀 To determine the quadrant of a point, observe the signs of its coordinates: (+,+) for Quadrant I, (-,+) for Quadrant II, (-,-) for Quadrant III, and (+,-) for Quadrant IV.
• 😀 The intersection of the coordinate axes creates four regions called quadrants, which help in identifying the location of points in the Cartesian plane.

Q & A

What is the Cartesian coordinate system?

The Cartesian coordinate system, also known as the rectangular coordinate system, is a two-dimensional system used for graphing ordered pairs, where two perpendicular number lines (x-axis and y-axis) intersect at the origin.

Who developed the Cartesian coordinate system?

The Cartesian coordinate system was developed by the French mathematician, philosopher, and theologian René Descartes, who lived from 1596 to 1650.

What is the significance of the origin in the Cartesian plane?

The origin is the point where the x-axis and y-axis intersect, and it has coordinates (0, 0), serving as the reference point for all other points in the Cartesian coordinate system.

How are the quadrants in the Cartesian plane defined?

The Cartesian plane is divided into four quadrants based on the signs of the x and y coordinates: Quadrant I (positive, positive), Quadrant II (negative, positive), Quadrant III (negative, negative), and Quadrant IV (positive, negative).

What are the coordinates of points in Quadrant I?

In Quadrant I, both the x and y coordinates are positive, meaning any ordered pair in this quadrant will have positive values for both coordinates.

What is the difference between abscissa and ordinate?

The abscissa refers to the x-coordinate of an ordered pair, while the ordinate refers to the y-coordinate.

How do you plot a point on the Cartesian plane?

To plot a point, start at the origin (0, 0). Move horizontally to the x-coordinate value (right for positive, left for negative) and then move vertically to the y-coordinate value (up for positive, down for negative).

What is the significance of signs in determining the quadrant of a point?

The signs of the x and y coordinates determine the quadrant in which the point lies: positive x and positive y indicate Quadrant I, negative x and positive y indicate Quadrant II, negative x and negative y indicate Quadrant III, and positive x and negative y indicate Quadrant IV.

What does it mean for a point to lie on an axis?

If a point lies on an axis, it means one of its coordinates is zero. For example, points on the x-axis have a y-coordinate of 0, while points on the y-axis have an x-coordinate of 0.

What are the coordinates of the following locations: church, hospital, school, and market?

The coordinates for the mentioned locations are as follows: Church (–6, 5), Hospital (5, 1), School (3, 0), Market (0, 4).