Topicm3e39a375e277d864_1528449000663_0Topic

Central symmetrycentral symmetryCentral symmetry with respect to the origin of the coordinate system

Levelm3e39a375e277d864_1528449084556_0Level

Third

Core curriculumm3e39a375e277d864_1528449076687_0Core curriculum

X. Analytic geometry on the Cartesian plane. The student:

7) plots the circles and polygons in axial symmetrysymmetrysymmetry with respect to the coordinate system, central symmetrycentral symmetrycentral symmetry (with the center in the origin of the coordinate system).

Timingm3e39a375e277d864_1528449068082_0Timing

45 minutes

General objectivem3e39a375e277d864_1528449523725_0General objective

Interpretation and the use of information presented both in a mathematical and popular science texts also using graphs, diagrams and tables.

Specific objectivesm3e39a375e277d864_1528449552113_0Specific objectives

1. Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

2. Determining the central symmetrycentral symmetrycentral symmetry with respect to the origin og the coordinate system.

3. Plotting symmetrical figures with respect to the origin of the coordinate system.

Learning outcomesm3e39a375e277d864_1528450430307_0Learning outcomes

The student:

- determines the central symmetrycentral symmetrycentral symmetry with respect to the origin of the coordinate system,

- plots symmetrical figures with respect to the origin of the coordinate system.

Methodsm3e39a375e277d864_1528449534267_0Methods

1. Learning stations.

2. Situation analysis.

Forms of workm3e39a375e277d864_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm3e39a375e277d864_1528450127855_0Introduction

The students work in small groups. Using the technique of learning station they recollect methods of obtaining figures in the central symmetrycentral symmetrycentral symmetry.

Tasks for the stations.

Station 1 A right triangletriangletriangle with legs measuring 3 cm and 5 cm is given. Draw this triangle in the central symmetrycentral symmetrycentral symmetry with respect to pointpointpoint S inside this triangle.

Station 2 A right triangle with legs measuring 3 cm and 5 cm is given. Draw this triangletriangletriangle in the central symmetry with respect to point S outside this triangle.

Station 3 A right triangletriangletriangle with legs measuring 3 cm and 5 cm is given. Draw this triangle in the central symmetrycentral symmetrycentral symmetry with respect to pointpointpoint S being the center of the hypotenuse of this triangle.

Finally, the students present results of their work.

The teacher explains any doubts.

Procedurem3e39a375e277d864_1528446435040_0Procedure

The teacher informs the students that the aim of this class is getting to know the properties of the central symmetrycentral symmetrycentral symmetry with respect to the origin of the coordinate system.

Task The students think how to determine the coordinates of a pointpointpoint in the central symmetrycentral symmetrycentral symmetry with respect to the origin of the coordinate system. They formulate hypotheses and conclusions. Then, they check them using the interactive presentation.

[Slideshow]

The conclusion that should be formulated by the students:

- The image of point A (x, y) point in the central symmetry with respect to the origin of the coordinate system O (0, 0) is point A1 (-x, -y).
- Point O (0, 0) is called the origin of the coordinate system.m3e39a375e277d864_1527752263647_0- The image of point A (x, y) point in the central symmetry with respect to the origin of the coordinate system O (0, 0) is point A1 (-x, -y).
- Point O (0, 0) is called the origin of the coordinate system.

The students use the information to solve the tasks.

Task
Points A (4, -8) and B (8, -2) are ends of the line segmentline segmentline segment AB. Draw in the coordinate system line segment AIndeks dolny 1₁BIndeks dolny 1₁ symmetrical to line segmentline segmentline segment AB with respect to the origin of the coordinate system. Give the coordinates of points AIndeks dolny 1₁ i BIndeks dolny 1₁. What is the position of the line segments in relation to each other with respect to the origin of the coordinate system?

Task
Points A (-3, 2), B (1, -3), C (-1, -2) are apices of triangletriangletriangle ABC. Draw triangle AIndeks dolny 1₁BIndeks dolny 1₁CIndeks dolny 1₁ symmetrical to ABC with respect to the origin of the coordinate system. Give the coordinates of points AIndeks dolny 1₁, BIndeks dolny 1  Indeks dolny koniec₁ and CIndeks dolny 1₁.

Task
Points A (-4, 2) i B (-2, 6) are given. Point M is the center of the line segment AB. Find the coordinates of point MIndeks dolny 1₁, which is the image of point M in symmetry with respect to the origin of the coordinate system.m3e39a375e277d864_1527752256679_0Points A (-4, 2) i B (-2, 6) are given. Point M is the center of the line segment AB. Find the coordinates of point MIndeks dolny 1₁, which is the image of point M in symmetry with respect to the origin of the coordinate system.

Task 
Read the coordinates of points A, B, C, D, E, F and G from the graph. Find the images of these points in symmetrysymmetrysymmetry with respect to the origin of the coordinate system.

[Illustration 1]

Having solved all the tasks, the students present their results. The teacher assesses their work and explains any doubts.

An extra task Points A (2a+1, 2a‑b) and B (a+b, 3a+b) are given. Plot a and b so that points A and B are symmetrical with respect to the origin of the coordinate system. Answer: a = 0, b = - 1.

Lesson summarym3e39a375e277d864_1528450119332_0Lesson summary

The students do the consolidation tasks.

They work together to recapitulate the class and formulate the conclusion to be remembered.

- The image of point A (x, y) point in the central symmetry with respect to the origin of the coordinate system O (0, 0) is point A1 (-x, -y).
- Point O (0, 0) is called the origin of the coordinate system.m3e39a375e277d864_1527752263647_0- The image of point A (x, y) point in the central symmetry with respect to the origin of the coordinate system O (0, 0) is point A1 (-x, -y).
- Point O (0, 0) is called the origin of the coordinate system.

Selected words and expressions used in the lesson plan

center of symmetrycenter of symmetrycenter of symmetry

center of the line segmentcenter of the line segmentcenter of the line segment

central symmetrycentral symmetrycentral symmetry

figures symmetrical with respect to the origin of the coordinate systemfigures symmetrical with respect to the origin of the coordinate systemfigures symmetrical with respect to the origin of the coordinate system

image of a point in central symmetryimage of a point in central symmetryimage of a point in central symmetry

line segmentline segmentline segment

pointpointpoint

quadranglequadranglequadrangle

symmetrysymmetrysymmetry

triangletriangletriangle