"Plane Cartesian Coordinate System" PPT Courseware 6

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"Plane Cartesian Coordinate System" PPT Courseware 6

Import new knowledge

This forms a plane Cartesian coordinate system.

New knowledge 1: What is a plane rectangular coordinate system?

Two numerical axes with a common origin and perpendicular to each other on the plane form a plane rectangular coordinate system, referred to as the rectangular coordinate system.

The horizontal number axis is called the x-axis or horizontal axis.

The vertical number axis is called the y-axis or vertical axis.

(They are collectively called coordinate axes)

The common origin O is called the coordinate origin.

New Knowledge 2: How many parts does the X-axis and Y-axis divide the plane into? What are they called?

Note: Points on the coordinate axes do not belong to any quadrant.

Given the position of a point, how to determine the coordinates of the point

How to determine the coordinates of point P?

Method: First draw a vertical line to the horizontal axis,

The number corresponding to the vertical foot is the abscissa of the point.

Then draw a vertical line to the vertical axis,

The number corresponding to the vertical foot is the ordinate of the point.

The coordinates of Q are (m, n). How to determine the position of Q?

1. Draw a perpendicular to the x-axis through the point representing m on the x-axis.

2. Draw the vertical line of the y-axis through the point representing n on the y-axis.

3. The intersection of the two lines is point Q.

Typical examples

Example 1. The coordinates of point P are known to be (a-1, a-5)

①Point P is on the x-axis, then a=____;

∵Point P is on the X-axis

∴The ordinate of point P is 0, that is, a-5=0

∴a=5

②Point P is on the y-axis, then a=____;

③If a=-3, then P is in the ____ quadrant;

④If a=3, then point P is in the ____ quadrant.

Example 2, as shown in the figure, (1) write the coordinates of points A, B, and C;

(2) Find the area of ​​△ABC.

Summary of this section

In this lesson we learned about the plane rectangular coordinate system. To study this section we need to master the following three aspects of knowledge:

1. Able to draw the rectangular coordinate system correctly.

2. Able to find points based on coordinates in the Cartesian coordinate system and obtain coordinates from points. There is a one-to-one correspondence between points in the coordinate plane and ordered pairs of real numbers.

3. Master the characteristics of the coordinates of quadrant points, x-axis and y-axis points:

The first quadrant: (+, +) The second quadrant: (-, +)

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

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)

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Update Time: 2024-10-03

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