CARTESIAN COORDINATES
Definition Of Cartesian Coordinates
Cartesian Coordinate System consists of two axes, X and Y, which intersect each other at a point called `origin`, and is used to define the position of any point by using ordered pairs.
More About Cartesian Coordinates
In two-dimensional coordinate system, the reference of a point is given by using two coordinates, X and Y.
In three-dimensional coordinate system, the reference of a point is given by using three coordinates, X, Y, and Z.
Video Examples: Math - Cartesian Coordinate System
Example of Carroll Diagram
Four points are marked on the Cartesian coordinate system: (3, 2) in blue, (- 2, 3) in red, (- 1, - 2) in brown, and (2, - 3) in green
Solved Example on Carroll Diagram
Ques: Which of the given coordinates represents the point marked on the coordinate plane?
Choices:
A. (3, 4)
B. (1, 1)
C. (2, 6)
D. (2, 5)
Correct Answer: D
Solution:
Step 1: The point is 2 units to the right of the Y-axis.
Step 2: So, the X-coordinate is 2.
Step 3: The point is 5 units above the X-axis.
Step 4: So, the Y-coordinate is 5.
Step 5: The coordinates of the point marked on the coordinate plane are (2, 5).
Quick Summary
- Cartesian Coordinates use two axes (X and Y) intersecting at the origin.
- Points are defined by ordered pairs (X, Y) in 2D and (X, Y, Z) in 3D.
- The X-coordinate represents the horizontal distance from the origin.
- The Y-coordinate represents the vertical distance from the origin.
🍎 Teacher Insights
Use graph paper to help students visualize the coordinate plane. Start with simple examples and gradually increase the complexity. Emphasize the importance of accurate plotting and reading of coordinates. Use real world examples such as map reading.🎓 Prerequisites
- Basic Algebra
- Number Lines
- Axes
Check Your Knowledge
Q1: What are the coordinates of the origin?
Q2: In which quadrant is the point (-2, 3) located?
Frequently Asked Questions
Q: What is the origin in the Cartesian coordinate system?
A: The origin is the point where the X and Y axes intersect, represented by the coordinates (0, 0).
Q: How do you plot a point given its coordinates?
A: Start at the origin, move horizontally along the X-axis according to the X-coordinate, and then move vertically along the Y-axis according to the Y-coordinate.