Here is a concise summary of the provided text:
**Topic:** Introduction to the Cartesian Plane
**Key Points:**
1. **Cartesian Plane Composition:**
* Formed by two perpendicular axes (90° angle)
* Horizontal axis (x-axis, abscissas)
* Vertical axis (y-axis, ordinates)
2. **Point Representation:**
* Points are determined by **ordered pairs** (x, y)
* Order matters (e.g., (3, 2) ≠ (2, 3))
3. **Axes and Quadrants:**
* **Axes:**
+ Points on x-axis have y=0
+ Points on y-axis have x=0
* **Quadrants:**
1. (+x, +y)
2. (-x, +y)
3. (-x, -y)
4. (+x, -y)
4. **Bisectors:**
* **Bisector of Quadrants 1 and 3:** x = y (e.g., (2, 2))
* **Bisector of Quadrants 2 and 4:** x = -y (e.g., (1, -1))
**Conclusion:**
A brief introduction to the Cartesian Plane, covering its composition, point representation, axes, quadrants, and bisectors.
Here are the key facts extracted from the text, numbered and in short sentences, without opinions:
**Cartesian Plane Basics**
1. The Cartesian plane is formed by two axes: a horizontal axis (x-axis) and a vertical axis (y-axis).
2. The x-axis and y-axis form a 90-degree angle.
3. The x-axis is also known as the axis of abscissas.
4. The y-axis is also known as the axis of ordinates.
**Points on the Cartesian Plane**
5. Points on the plane are determined by ordered pairs (x, y).
6. The order of the pair matters (e.g., (3, 2) ≠ (2, 3)).
7. The first element of the pair represents the x-coordinate.
8. The second element of the pair represents the y-coordinate.
**Quadrants**
9. The Cartesian plane is divided into four regions called quadrants.
10. The quadrants are numbered 1 to 4 in a counterclockwise direction.
11. Quadrant 1: (+x, +y), Quadrant 2: (-x, +y), Quadrant 3: (-x, -y), Quadrant 4: (+x, -y)
**Points on Axes**
12. A point on the x-axis has a y-coordinate of 0.
13. A point on the y-axis has an x-coordinate of 0.
**Bisectors**
14. The bisector of the 1st and 3rd quadrants is a line that divides these quadrants in half, at a 45-degree angle.
15. Points on this bisector have equal x and y values (but may differ in sign).
16. The bisector of the 2nd and 4th quadrants is a line where points have equal x and y values in modulus, but differ in sign (e.g., (a, -a)).