"Plane Cartesian Coordinate System" PPT courseware 7

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"Plane Cartesian Coordinate System" PPT courseware 7

Knowledge review: What is a number line?

Specifying the origin, positive direction, and unit length on a straight line constitutes a number axis.

A point on the number axis can be represented by a number, which is called the coordinate of the point. For example, the coordinate of point A on the number axis is -3, and the coordinate of point B on the number axis is 4. Conversely, knowing the coordinates of a point on the number axis, the position of this point on the number axis is also determined.

Think about it?

Similar to using a number axis to determine the position of a point on a straight line, can we find a way to determine the position of a point in a plane?

(For example, points A, B, C, and D in the picture)?

Create a rectangular coordinate system

With the plane rectangular coordinate system, points in the plane can be represented by an ordered number pair. The coordinates of the origin are (0, 0).

Communication and discovery:

Think: What characteristics do the points in each quadrant have?

Expansion and extension: What are the characteristics of the points on the horizontal and vertical coordinate axes?

Summary and improvement

The coordinates of the origin are (0, 0)

First quadrant (+, +) Second quadrant (-, +)

The third quadrant (-, -) the fourth quadrant (+, -)

The ordinate of any point on the x-axis is 0, denoted as (x, 0).

The abscissa coordinate of any point on the y-axis is 0, denoted as (0, y).

practise:

1. Fill in the blanks:

(1) The coordinates of the symmetry point of point P (3, -4) about the origin are ______; the coordinates of the symmetry point about the x-axis are _____;

The coordinates of the symmetry point about the y-axis are ________

(2) Two points A (a, 6) and B (2, b) are known.

①When A and B are symmetrical about the x-axis, a=_____; b=_____.

②When A and B are symmetrical about the y-axis, a=_____; b=_____.

③When A and B are symmetrical about the origin, a=_____; b=_____

2. Multiple choice questions

(1) If point M (x, y) satisfies x+y=0, then point M is located at ( )

(A) The bisector of the angle between the two coordinate axes in the first and third quadrants

(B) On the x-axis (C) On the x-axis

(D) The bisector of the angle between the two coordinate axes in the second and fourth quadrants

(2) The distance from point P (a, b) in the fourth quadrant to the x-axis is ()

(A)a (B)-a (C)-b (D)b

(3) Point A (-m, 1-2m) is a symmetrical point about the origin in the first quadrant, then the value range of m is (　)

(A)m>0.5 (B)m<0.5 (C)m>0 (D)m<0

Classroom section

What did you gain from studying this class?

1. How to establish a plane rectangular coordinate system

2. Draw the position of the point based on the coordinates, and determine the coordinates of the point based on the position of the point.

3. Know the characteristics of the coordinates of points on the polar coordinate axis within the quadrant

4. The idea of ​​combining numbers and shapes

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Update Time: 2024-10-13

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