"Axisymmetric and Coordinate Changes" Position and Coordinates PPT Teaching Courseware

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"Axisymmetric and Coordinate Changes" Position and Coordinates PPT Teaching Courseware

Part One: Learning Objectives

1. Explore the process of changing graphics coordinates. (Key points)

2. Grasp the relationship between changes in graphic coordinates and axial symmetry of the graphic. (Difficulty)

Axial symmetry and coordinate changes PPT, Part 2: Importing new lessons

Review introduction

1.What is an axially symmetrical figure?

A figure that is folded in half along a straight line and the parts on both sides of the straight line can completely overlap is an axially symmetric figure; this straight line is called the axis of symmetry.

2. How to determine the position of point P in the plane Cartesian coordinate system?

a is called the abscissa of point P,

b is called the ordinate of point P.

Axial symmetry and coordinate changes PPT, part 3: teaching new lessons

Axial symmetry and coordinate changes

Explore the coordinate relationship between one and two figures that are symmetrical about the coordinate axis

1. △ABC and △A1B1C1 are in the rectangular coordinate system as shown in the figure. Observe carefully and complete the following questions:

(1) What is the positional relationship between △ABC and △A1B1C1?

△ABC and △A1B1C1 are symmetrical about the x-axis

(2) Please fill in the coordinates of points A and A1, points B and B1, and points C and C1 in the table below, and think about: What is the relationship between the coordinates of these corresponding points?

(3) If point P (m, n) is in △ABC, then the coordinates of its corresponding point P1 in △A1B1C1 are _________.

2. In the plane rectangular coordinate system shown on the right, there is a small flag in the first and second quadrants.

(1) What is the positional relationship between the two small flags?

Axisymmetric about the y-axis

(2) Please fill in the coordinates of points A and A1, points B and B1, points C and C1, points D and D1 in the table below, and think: What is the relationship between the coordinates of these corresponding points?

(3) If point P (m, n) is in △ABC, then the coordinates of its corresponding point P1 in △A1B1C1 are _________.

3. Through the above study, do you know the relationship between the coordinates of two points that are symmetrical about the x-axis? What about the relationship between the coordinates of two points that are symmetric about the y-axis?

In conclusion

1. Coordinate characteristics of points on two figures that are symmetrical about the y-axis:

The abscissas are opposite numbers to each other, and the ordinates are the same.

2. Coordinate characteristics of points on two figures that are symmetrical about the x-axis:

The abscissas are the same and the ordinates are opposite numbers to each other.

Axial symmetry and coordinate changes PPT, Part 4: Practice in class

1. The coordinates of point A (2, - 3) that are symmetrical about the x-axis are _________.

2. The coordinates of point B (-2, 1) that are symmetrical about the y-axis are _________.

3. The relationship between point (4, 3) and point (4, - 3) is ( )

A. Symmetric about the origin B. Symmetric about the x-axis

C. Symmetrical about the y-axis D. Cannot form a symmetrical relationship

4. Point (m, - 1) and point (2, n) are symmetrical about the x-axis, then m n is equal to ( )

A.- 2 B.2 C.1 D.- 1

5. It is known that the coordinates of points A and B are (-2, 3) and (2, 3) respectively.

Then the following four conclusions: ①A and B are symmetrical about the x-axis; ②A and B are symmetrical about the y-axis; ③A and B are symmetrical about the origin; ④The distance between A and B is 4. The correct ones are ( )

A． 1 B. 2 c. 3 D. 4

6. A beam of light starts from point A (3, 3), is reflected by point C on the y-axis, and then passes through point B (1, 0). Then the length of the route the light passes from point A to point B is ( )

A.4 B.5 C.6 D.7

Axial symmetry and coordinate changes PPT, Part 5: Class summary

Symmetric about the coordinate axis

Drawing - symmetrical changes about the axis

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For more information about the "Position and Coordinate Axis Symmetry and Coordinate Change" PPT courseware, please click the Position and Coordinate PPT Axis Symmetry and Coordinate Change PPT tag.

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Update Time: 2024-09-17

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