"Plane Cartesian Coordinate System" Position and Coordinates PPT Courseware 2

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"Plane Cartesian Coordinate System" Position and Coordinates PPT Courseware 2

Draw a rectangular coordinate system, find the following points in the drawn coordinate system, and connect the points with line segments. Observe what special positional relationship does point A have with other points?

A(-1,2),B(1,2)

C(-1,-2), D(1,-2)

Do you want to explore mysterious treasures?

In a "treasure hunt" game, the treasure hunter has found two landmark points with coordinates (3, 2) and (3, -2), and knows that the coordinates of the treasure location are (4, 4). Know other information. How to determine the Cartesian coordinate system to find the "treasure"? Communicate with peers.

Do it

Example 1 As shown in the figure, the length and width of rectangle ABCD are 6 and 4 respectively. Establish an appropriate coordinate system and write the coordinates of each vertex.

Solution: As shown in the figure, a rectangular coordinate system is established with point C as the origin of the coordinates, and the straight lines where CD and CB are located as the x-axis and y-axis. At this time, the coordinates of point C are (0, 0).

Since the length of CD is 6 and the length of CB is 4, the coordinates of D, B, and A can be obtained as D(6, 0), B(0, 4), and A(6, 4) respectively.

Discuss

1. In the above example, how else can you establish a rectangular coordinate system?

2. How do you think a suitable rectangular coordinate system should be established?

There is no hard and fast model, but choosing an appropriate coordinate system can make calculations less difficult!

In a "treasure hunt" game, the treasure hunter has found two landmark points with coordinates (3, 2) and (3, -2), and knows that the coordinates of the treasure location are (4, 4). Knowing other information, how to determine the "treasure" you are looking for in the Cartesian coordinate system? Can you find it? Communicate with your peers.

Tips: Connect the two landmark points, draw the mid-perpendicular line of the resulting line segment, and use this line as the horizontal axis.

summary:

1. There is a one-to-one correspondence between points in the coordinate plane and ordered pairs of real numbers.

2. Given a point in the coordinate plane, the quadrant or coordinate axis where it is located can be used to describe the position of the point in the plane.

3. Remember the symbols of the coordinates of points in each quadrant, and find the symmetry point of a known point about the coordinate axis or origin based on the knowledge of symmetry.

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Update Time: 2024-07-03

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