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"Plane Cartesian Coordinate System" PPT Courseware 3
What are the symbolic characteristics of the coordinates of the points in each quadrant? What are the characteristics of the coordinates of points on the coordinate axis?
Activity 1: Draw the following points in the Cartesian coordinate system: A (3,2) B (3,-2) C (-3,2) D (-3,-2) E (0,4) F (0 ,-4)G (4,0) H (-4,0)
discuss:
Characteristics of the coordinate symbols of the quadrant midpoint:
The symbols of the coordinates in the first, second, third and fourth quadrants are (+,+), (-,+), (-,-), (+, -) respectively.
Characteristics of point coordinates on the coordinate axis:
The ordinate of the point on the horizontal axis is 0, expressed as (x, 0)
The abscissa coordinate of the point on the vertical axis is 0. It is expressed as (0, y)
The coordinates of the origin are (0,0)
What are the distances from points A, B, C, and D to the X-axis and y-axis? What patterns did you discover?
law:
The distance from a point to the X-axis is the absolute value of the ordinate of the point
The distance from a point to the Y-axis is the absolute value of the abscissa of the point
Talk about it
Please quickly tell the distance from each of the following points to the x-axis and y-axis
A (4, -2) B (0, 3) C (3, 4)
D (-4,-3) E (-2, 0) F (-4, 3)
What is the symmetry between point A and points B, C, and D, and what is the connection between their coordinates?
Point A and point B are symmetrical about the X-axis
The abscissas are the same and the ordinates are opposite numbers to each other.
Point A and point C are symmetrical about the Y axis
The ordinates are the same and the abscissas are opposite numbers to each other.
Point A and point D are symmetrical about the origin
The abscissa and ordinate are opposite numbers to each other.
practice
If we set point M(a,b),
The symmetry point M1 of point M about the X axis ( )
The symmetry point M2 of point M about the Y axis ( )
The symmetry point M3 of point M about the origin O ( )
Knowledge interactive point pairing:
1. Point (3, -2) is in the _____ quadrant; point (-1.5, -1) is in the _______ quadrant; point (0, 3) is on the ____ axis;
If the point (a+1,-5) is on the y-axis, then a=______.
2. The distance from point M (-8, 12) to the x-axis is ________, and the distance to the y-axis is ________.
3.The symmetry point of point A(-2,4) about the x-axis is _________.
4. Point A is on the x-axis, 4 units in length from the origin, then the coordinates of point A are ___________.
in conclusion:
Characteristics of coordinates of points that are symmetrical about coordinate axes and origins
Two points that are symmetrical about the X-axis have the same abscissa and opposite ordinates.
Two points that are symmetrical about the Y axis have the same vertical coordinates and opposite horizontal coordinates.
For two points that are symmetrical about the origin, the abscissa and ordinate are opposite numbers to each other.
Review and Thoughts
1. What is a plane rectangular coordinate system?
2. The coordinate axis divides the plane into four parts. What are they called?
3. How to find the coordinates of a point in the plane?
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