CARTESIAN PLANE
Definition Of Cartesian Plane
A Cartesian Plane is a plane consisting of a set of two lines intersecting each other at right angles. The horizontal line is the X-axis and the vertical one is the Y-axis, and the point of their intersection is called the origin with the coordinates (0, 0).
More About Cartesian Plane
The location of any point on the coordinate plane is denoted by using pair of coordinates (X, Y), where X is the horizontal distance from the origin and Y is the vertical distance from the origin.
The X and Y-axis on the coordinate plane is always perpendicular to each other.
Video Examples: Math Tutorial - Cartesian Plane
Example of Cartesian Plane
The location of point P is (4, 3), as the point P is placed 4 units (away from the origin) horizontally and 3 units (away from the origin) vertically.
Solved Example on Cartesian Plane
Ques: Identify the coordinates of the point C on the graph.
Choices:
A. (- 5, 1)
B. (5, - 1)
C. (- 1, - 5)
D. (- 5, - 1)
Correct Answer: D
Solution:
Step 1: Start at the origin.
Step 2: The point C is 5 units to the left from the Y-axis.
Step 3: So, the X-coordinate of point C is - 5.
Step 4: Point C is 1 unit below the X-axis.
Step 5: So, the Y-coordinate of point C is - 1.
Step 6: The coordinates of the point C are (- 5, - 1).
Quick Summary
- The Cartesian plane is defined by two perpendicular axes: the X-axis (horizontal) and the Y-axis (vertical).
- Points on the plane are located using ordered pairs (X, Y), where X is the horizontal distance and Y is the vertical distance from the origin.
- The point of intersection of the X and Y axes is called the origin and has coordinates (0, 0).
⚠️ Common Mistakes
- Reversing the order of coordinates (X, Y).
- Confusing positive and negative directions on the axes.
- Misinterpreting the scale of the axes.
📋 Standards Alignment
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🍎 Teacher Insights
Use visual aids and real-world examples to illustrate the concept of coordinates. Emphasize the importance of the order of the coordinates (X, Y).🎓 Prerequisites
- Basic arithmetic
- Number lines
- Understanding of positive and negative numbers
Check Your Knowledge
Q1: What are the coordinates of the origin?
Q2: In the ordered pair (3, -2), which value represents the x-coordinate?
Frequently Asked Questions
Q: What is the origin?
A: The origin is the point where the X and Y axes intersect. It has coordinates (0, 0).
Q: How do I find a point on the Cartesian plane?
A: Start at the origin. Move horizontally according to the X-coordinate and then vertically according to the Y-coordinate.