"Review" Plane Cartesian Coordinate System PPT Courseware

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"Review" Plane Cartesian Coordinate System PPT Courseware

1. Review purpose:

1. Understand the meaning of the plane rectangular coordinate system and master the coordinate characteristics of points in each quadrant. Master the method of finding the coordinates of some special points.

2. Be able to establish an appropriate plane rectangular coordinate system to describe the position of an object. In the same rectangular coordinate system, feel the changes in the coordinates of the points after the graphics transformation.

3. In the plane rectangular coordinate system, the translation transformation can be expressed by coordinates.

(2) Classification and application of knowledge points in this chapter:

1. The meaning of the plane rectangular coordinate system and the composition of the coordinate plane:

(1) Two ______ in the plane that ______ each other and the origin ______ form a plane rectangular coordinate system. Among them, the horizontal number axis is called ______ or ______, and it is customary to take ______ as the positive direction; the vertical number axis is called ______ or ______, and the ______ direction is taken as the positive direction; the two coordinate axes The intersection point is called ______ of the plane Cartesian coordinate system. The ______ where the rectangular coordinate system is located is called the coordinate plane.

(2) After the plane rectangular coordinate system is established, the coordinate plane is ______ divided into four parts I, II, III, and IV, as shown in the figure, called ______, ______, ______, ______ respectively. Note that the points on ______ do not belong to any quadrant.

(1): Find coordinates from points

Method: Draw vertical lines through the known points to the x-axis and y-axis respectively. The corresponding numbers on the number axis are the abscissa and ordinate of the point.

(2): Find points by coordinates

Method: First find the points representing the abscissa and ordinate on the x-axis and y-axis respectively, and then draw vertical lines through these two points respectively for the x-axis and y-axis. The intersection of the two vertical lines is the point corresponding to the coordinates.

Consolidation exercise 1: Find quadrants from coordinates.

(1) The coordinates of point P are (2,-3), then point P is in the ______ quadrant;

(2) If the coordinates of point P (x, y) satisfy xy�0, then point P is in the ______ quadrant;

(3) If the coordinates of point P (x, y) satisfy xy�0 and are above the x-axis, then point P is in the ______ quadrant;

(4) If the coordinates of point A are (a2+1, -2–b2), then point A is in the ____ quadrant.

Warm reminder: To judge the position of a point, the key is to grasp the symbolic characteristics of the ______ coordinates of the point in the quadrant.

Points on the bisectors of quadrant angles

1. It is known that point A (2, y), point B (x, 5), points A and B are on the angle bisector of the first and third quadrants, then x =____, y =____;

2. It is known that point A (2a+1, 2+a) is on the bisector of the second quadrant, try to find the coordinates of A.

3. It is known that point M (a+1, 3a-5) is on the bisector of the angle between the two coordinate axes. Try to find the coordinates of M.

Consolidation exercises:

(1). If the coordinates of point A are (- 3, 5), then its distance to the x-axis is ______, and its distance to the y-axis is ______.

(2).The distances from point P to the x-axis and y-axis are 2,1 respectively, then the coordinates of point P may be ______.

test you

1. In the plane rectangular coordinate system, there is a point P (-5, 3). If P:

(1) Translate 2 units to the left, and the coordinates of the obtained point are ______;

(2) Translate 3 units to the right, and the coordinates of the obtained point are ______;

(3) Translate downward by 4 units of length, and the coordinates of the obtained point are ______;

(4) First translate 5 units to the right, and then 3 units upward. The resulting coordinates are _______.

2. If the coordinates of A and B are A (-4, 5) and B (-4, 2) respectively, translate point A to ___ by ___ unit length to obtain point B; move point B to __ _Translate___ units of length to get point A.

3. If the coordinates of P and Q are P (-3, -5) and Q (2, -5) respectively, translate point P to ___ by ___ unit length to obtain point Q; move point Q to _ __Translate___ units of length to get point P.

4. Point P (x, y) is in the fourth quadrant, and |x|=3, |y|=2, then the coordinates of point P are _______.

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Update Time: 2024-10-02

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