"Plane Cartesian Coordinate System" PPT courseware 4

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"Plane Cartesian Coordinate System" PPT courseware 4

1: How to determine the position of a point on a straight 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 on the number axis. For example, the coordinate of point A on the number axis is -3, and the coordinate of point B on the number axis is 2. Conversely, knowing the coordinates of a point on the number axis, the position of this point on the number axis is also determined.

2. How to determine the position of a point in the plane?

We already know that the position of a point in the plane can be represented by an ordered number pair, so can we use two number axes to solve this problem?

NO.1 Cartesian coordinate system: Concept (Page 168)

Draw two mutually perpendicular number axes with a common origin (that is, the origins coincide) in the plane to form a plane rectangular coordinate system, referred to as the rectangular coordinate system. The number axis in the horizontal direction is called the x-axis or the horizontal axis, and the direction oriented to the right is the positive direction. The number axis in the vertical direction is called the y-axis or the vertical axis, and the direction oriented upward is the positive direction. The x-axis and the y-axis are collectively called the coordinate axes, and their common origin is called the coordinate origin, or the origin for short. Generally represented by O.

NO.2 Quadrant: (Page 168)

Note: The points on the coordinate axis do not belong to any quadrant

NO.3 coordinates (1) P169:

How to determine the coordinates of a point?

The number represented by the perpendicular foot M on the x-axis of the x-axis and the y-axis passing through the point A is -2, and the number represented by the vertical foot N on the y-axis is 3. We say that the abscissa of A is - 2, the ordinate is 3.

The ordered number pair (-2,3) is the coordinate of point A marked as A (-2,3), and the origin of the point is marked as (0,0) M (-2,0), N (0,3)

Note: The abscissa is written before and the ordinate is written after, separated by commas.

What are the characteristics of the coordinates of points on the coordinate axis?

in conclusion

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. Expressed as (0, y), the coordinate of the origin is (0,0)

What are the characteristics of the coordinates of a point on a straight line parallel to a coordinate axis?

in conclusion

Points on a straight line parallel to the y-axis have the same abscissa, and points on a straight line parallel to the x-axis have the same ordinate.

practice

1. In the plane rectangular coordinate system, the following points are in the fourth quadrant ( )

A.(2,1) B.(-2,1) C.(-3,-5) D.(3,-5)

2. It is known that point A(m,n) in the coordinate plane is in the fourth quadrant, then point B(n,m) is in ( )

A. The first quadrant B. The second quadrant.

C. The third quadrant D. The fourth quadrant

3. Point P (3, a) is known, and the distance from point P to the x-axis is 2 units of length. Find the coordinates of point P.

Analysis: The distance from a point to the x-axis is the absolute value of the ordinate of the point, so the absolute value of a is equal to 2, so the value of a should be equal to ±2.

Solution: Because the distance from P to the X-axis is 2, the value of a can be equal to ±2, so P(3,2) or P(3,-2).

4. Let point M (a, b) be a point in the plane rectangular coordinate system

When a>0, b<0, which quadrant is point M located in?

When ab>0, in which quadrant is point M located?

When ab=0, where is point M?

When a is any number and b<0, what is the position of point M in the rectangular coordinate system?

Consolidation exercises:

1. Point (3, -2) is in the _____ quadrant; point (-1.5, -1)

In the _______ quadrant; point (0, 3) is on the ____ axis;

If the point (a+1,-5) is on the y-axis, then a=______.

2. Point A is on the x-axis, 4 units in length from the origin, then the coordinates of point A are ______________.

3. The distance from point M (-8, 12) to the x-axis is ________, and the distance to the y-axis is ________.

4. If point P is in the third quadrant and the distance to the x-axis is 2 and the distance to the y-axis is 1.5, then the coordinates of point P are _______.

Summary: This lesson mainly learns the properties of the plane rectangular coordinate system.

Related concepts and one of the most basic questions, points in the coordinate plane

There is a one-to-one correspondence with ordered number pairs.

1. Can find points based on coordinates and write coordinates from points in the coordinate system.

2. Master the characteristics of the coordinates of points on the x-axis and y-axis:

The ordinate of the point on the x-axis is 0, expressed as (x, 0)

The abscissa of the point on the y-axis is 0, expressed as (0, y)

First quadrant: (+, +)

Second quadrant: (-, +)

The third quadrant: (-,-)

Fourth quadrant: (+,-)

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"Plane Cartesian Coordinate System" Position and Coordinates PPT (Lesson 3):

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Update Time: 2024-09-16

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