"Plane Cartesian Coordinate System" Position and Coordinate PPT Courseware (Lesson 1)

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"Plane Cartesian Coordinate System" Position and Coordinate PPT Courseware (Lesson 1)

Part One Content: Basic Knowledge Key Points

Knowledge point 1: Plane rectangular coordinate system and related concepts

1. In the plane rectangular coordinate system, point A (3,-2) is at (D)

A. The first quadrant B. The second quadrant

C. The third quadrant D. The fourth quadrant

2. The distance from point P(3,4) to the x-axis is 4, the distance to the y-axis is 3, and the distance to the origin is 5.

Knowledge point 2: Determine the coordinates of the point

3. As shown in the figure, point A (-1,2), then the coordinates of point B are (D)

A.( -2,2 ) B.( -2,-3 )

C.( -3,-2 )D.( -2,-2 )

4. (Textbook Motif Variation) (1) Write the coordinates of points A, B, C, D, E, and F in the picture.

(2) Draw the following points on the graph: L( -5,-3 ), M( 4,0 ), N( 0,5 ), P( 6,2 ).

Solution: (1)A(-3,-2),B(-5,4),C(5,-4),D(0,-3),E(2,5),F(-3, 0 ).

(2) Figure omitted.

5. (Adapted) In the plane rectangular coordinate system, mark the positions of the following points and write the coordinates of each point.

(1) Point A is on the x-axis, located to the left of the origin, 4 units in length from the origin of the coordinates;

(2) Point B is on the y-axis, located on the upper side of the origin, 4 units in length from the coordinate origin;

(3) Point C is on the left side of the y-axis, on the upper side of the x-axis, and is 4 units in length from each coordinate axis.

Solution: (1) The figure is omitted, the coordinates of point A are (-4,0).

(2) The figure is omitted, the coordinates of point B are (0,4).

(3) The figure is omitted, the coordinates of point C are (-4,4).

Plane Cartesian Coordinate System PPT, Part 2: Improvement of Comprehensive Capabilities

6. In the square grid as shown in the figure, the coordinates of point A are (2,1), the coordinates of point B are (2,-1), then the coordinates of point P are (B)

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

7. As shown in the figure, there is a square divided into thirty-six small squares with an area of ​​1. Point A and point B are on two grid points. Ask whether there is a point C on the grid point, so that the area of ​​△ABC is 2, there are 5 such points C.

8. It is known that the abscissa of point A in the plane is -6, and the distance to the origin is equal to 10, then the coordinates of point A are (-6,8) or (-6,-8).

9. It is known that the distance from point P (2-a, 3a-2) to the two coordinate axes is equal. Then the coordinates of point P are (1,1) or (2,-2).

10. As shown in the figure, it is known that A1( 1,0 ), A2( 1,-1 ), A3( -1,-1 ), A4( -1,1 ), A5( 2,1 ),…, then point The coordinates of A2010 are (503,-503).

Plane Cartesian Coordinate System PPT, Part 3: Expansion, Research and Breakthroughs

14. [Reading materials] In the plane rectangular coordinate system, the absolute value of the abscissa coordinate x of point P (x, y) is expressed as |x|, and the absolute value of the ordinate y is expressed as | y|, we call the sum of the absolute values ​​of the abscissa and ordinate of point P(x,y) the Pythagorean value of point P(x,y), recorded as [P], that is [P]=|x|+|y|(where "+" is addition in the four arithmetic operations), such as Pythagorean at point P(1,2) Value[P]=|1|+|2|=3.

【Solve the problem】

(1) Find the Pythagorean values ​​[A],[B]; of points A(-2,4),B(√2+√3,√2−√3)

(2) If point M is above the x-axis, its horizontal and vertical coordinates are integers, and [M]=3, please write the coordinates of point M.

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Update Time: 2024-12-04

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