"Plane Cartesian Coordinate System" Position and Coordinate PPT Courseware (Lesson 2)

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"Plane Cartesian Coordinate System" Position and Coordinate PPT Courseware (Lesson 2)

Part One Content: Basic Knowledge Key Points

Knowledge point 1: Establish an appropriate plane rectangular coordinate system to find the coordinates of a point

1. As shown in the figure, there is an isosceles triangle ABC. Now we need to establish a plane rectangular coordinate system to find the coordinates of its vertices. What do you think is the most reasonable method? (A)

A. Taking the midpoint O of BC as the coordinate origin, the straight line where BC is located is the x-axis, and the straight line where AO is located is the y-axis.

B. Take point B as the coordinate origin, the straight line where BC is located is the x-axis, and the perpendicular line passing through point B as the x-axis is the y-axis.

C. Taking point A as the coordinate origin, the straight line parallel to BC is the x-axis, and the perpendicular line passing through point A as the x-axis is the y-axis.

D. With point C as the coordinate origin, the straight line parallel to BA is the x-axis, and the perpendicular line passing through point C as the x-axis is the y-axis.

2. In the rectangle ABCD, the coordinates of point A are (1,3), the coordinates of point B are (1,-2), the coordinates of point C are (-4,-2), then the coordinates of point D are ( -4,3 )　.

3. It is known that the length and width of rectangle ABCD are 6 and 4 respectively. Establish an appropriate plane rectangular coordinate system and write the coordinates of each vertex.

Solution: Establish a plane rectangular coordinate system as shown in the figure.

A( 0,4 ),B( 0,0 ),C( 6,0 ),D( 6,4 ).

Knowledge point 2: Characteristics of the coordinates of points in the plane rectangular coordinate system

4. In the plane rectangular coordinate system, the known point P(2,a) is in the fourth quadrant, then (A)

A.a<0 B.a≤0

C.a>0 D.a≥0

5. As shown in the figure, the coordinates of the point covered by the little hand may be (B)

A.(3,3) B.(-4,5)

C.(-4,-6)D.(3,-6)

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

8. It is known that m is any real number, then point A(m,m2+1) is not in (D)

A. The first and second quadrants B. The first and third quadrants

C. The second and fourth quadrants D. The third and fourth quadrants

9. In the plane rectangular coordinate system, point M is in the fourth quadrant, and the distances to the x-axis and y-axis are 6 and 4 respectively, then the coordinates of point M are (A)

A.(4,-6) B.(-4,6)

C.(6,-4) D.(-6,-4)

10. If a plane rectangular coordinate system is established with point B as the origin, and the coordinates of point A are (3,4), then a plane rectangular coordinate system is established with point A as the origin, and the coordinates of point B are (A)

A.( -3,-4 )B.( -3,4 )

C.(3,-4) D.(3,4)

11. If point P (m+3,m+1) is on the x-axis of the plane rectangular coordinate system, then the coordinate of point P is (B)

A.(0,-2) B.(2,0)

C.(4,0) D.(0,-4)

12. As shown in the figure, the straight line m⊥n is known. In a certain plane rectangular coordinate system, the x-axis ∥ straight line m, the y-axis ∥ straight line n, the coordinates of points A and B are (-4,2), (2, -4), points A, O4, and B are on the same straight line, then the origin of the coordinates is (A)

A.O1 B.O2 C.O3 D.O4

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

18. As shown in the figure, in Rt△OAB, the hypotenuse OB is on the positive half-axis of the x-axis, the right-angled vertex A is in the fourth quadrant, S△OAB=20, OA∶AB=1∶2, find A and B The coordinates of two points.

Solution: Draw AC⊥OB through point A, and draw the vertical foot as C.

Assume OA=x, then AB=2x.∵S△OAB=20,∴1/2AO·AB=20,

That is, x2=20, the solution is x=2√5, ∴OA=2√5, AB=4√5.

According to the Pythagorean theorem, OB=10, ∴The coordinates of point B are (10,0).

∵1/2OB•AC=20,∴5AC=20,∴AC=4.

In △OAC, according to the Pythagorean theorem, OC=2, and the coordinates of ∴ point A are (2,-4).

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Update Time: 2024-11-08

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