"Position Similarity" similar PPT courseware 4

Description

"Position Similarity" similar PPT courseware 4

learning target

1. Be able to use the change of the coordinates of the figure to represent the positional transformation of the figure, and master the rules of the change of the coordinates of the points after a figure is enlarged or reduced according to a certain size ratio;

2. Understand the similarities and differences of the four transformations (translation, axial symmetry, rotation and similarity), and be able to find these transformations in complex graphics.

New course introduction

1.What is a bit-like figure?

If two figures are not only similar, but also the lines connecting the corresponding vertices intersect at a point, the two figures are called similarity figures, and this point is called the similarity center. The similarity ratio at this time is also called the similarity ratio.

2. Properties of bit-like figures

The ratio of the distances between any pair of corresponding points on the similarity figure to the similarity center is equal to the similarity ratio

3. Use bitmap to enlarge or reduce a graphic

Knowledge explanation

In the plane rectangular coordinate system, there are two points A(6,3) and B(6,0), with the origin O as the similarity center, the similarity ratio is 1:3, and the line segment AB is reduced.

Observe the changes in coordinates between corresponding points. What do you find?

In the plane rectangular coordinate system, if the similarity transformation takes the origin as the similarity center and the similarity ratio is k, then the ratio of the coordinates of the corresponding points of the similarity figure is equal to k or -k.

In the plane rectangular coordinate system, the coordinates of the three vertices of △ABC are A(2,3), B(2,1), and C(6,2). With the origin O as the similarity center, the similarity ratio is 2. Draw its shape.

What are the coordinates of the corresponding points after zooming in?

A′(4,6), B′(4,2), C′(12,4)

example

[Example] In the plane rectangular coordinate system, the coordinates of the four vertices of the quadrilateral ABCD are A(-6,6), B(-8,2), C(-4,0), D(-2,4). ), draw a similarity figure with the origin O as the similarity center and a similarity ratio of 1/2.

A′( -3,3 ), B′( -4,1 ), C′( -2,0 ), D′( -1,2 )

Do you have any other ideas? Give it a try.

Practice in class

1. (Yulin High School Entrance Examination) As shown in the figure, double the three sides of △ABC to get △A1B1C1 (the vertices are all on the grid points). They are position-like figures with point P as the position-like center. Then the coordinates of point P yes( )

A. (�4,�3) B. (�3,�3)

C. (�4,�4) D. (�3,�4)

2. (Ningxia High School Entrance Examination) Regarding the expression of counterpoint-like figures, the following proposition is correct ________. (Just fill in the serial number)

① Similar figures must be similar figures in position, and similar figures in position must be similar figures;

② A similar figure must have a similar center;

③If two figures are similar figures, and the straight lines connecting each set of corresponding points pass through the same point, then the two figures are similar figures;

④The ratio of the distance between any two points on the similarity figure and the similarity center is equal to the similarity ratio.

【Answer】②,③

Summary of this lesson

In the plane rectangular coordinate system, if the similarity transformation takes the origin as the similarity center and the similarity ratio is k, then the ratio of the coordinates of the corresponding points of the similarity figure is equal to k or -k.

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Update Time: 2024-10-03

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 2 industry PPT template

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