ORIGIN
Definition Of Origin
The point of intersection of the altitudes of a triangle is called an orthocenter.
More About Origin
The coordinates of the origin are (0, 0).
Counting of the coordinates starts from the origin.
Example of Origin
In the figure, x and y axis are intersecting at 'O'.
This O is called the origin of the graph. Its coordinates are (0, 0).
Video Examples: Transformational Geometry Rotations around the Origin
Solved Example on Origin
Ques: Translate the book O (0, 0) down 3 units and right 4 units. What are the coordinates of its image O′?
Choices:
A. (4, - 3)
B. (3, - 4)
C. (- 3, 4)
D. (4, - 3)
Correct Answer: A
Solution:
Step 1: When (0, 0) is translated down 3 units, the y-coordinate becomes - 3, but the x-coordinate remains same.
Step 2: After translating (0, - 3) to 4 units right, the x-coordinate of the point becomes 4, but the y-coordinate remains same.
Step 3: So, the coordinates of the new point O' are (4, - 3).
Quick Summary
- The origin is the point (0, 0) on the coordinate plane.
- It is where the x-axis and y-axis intersect.
- All coordinates are measured relative to the origin.
🍎 Teacher Insights
Use visual aids and real-world examples to help students understand the concept of the origin. Emphasize that it is the starting point for graphing coordinates.🎓 Prerequisites
- Number lines
- Coordinate plane
- Positive and negative numbers
Check Your Knowledge
Q1: What are the coordinates of the origin?
Q2: If a point is translated 5 units to the right from the origin, what are its new coordinates?
Frequently Asked Questions
Q: What are the coordinates of the origin?
A: The coordinates of the origin are (0, 0).
Q: Why is the origin important?
A: The origin is the reference point for locating all other points on the coordinate plane.