Topicm525a71978336c822_1528449000663_0Topic

Translating a point in the coordinate system

Levelm525a71978336c822_1528449084556_0Level

Third

Core curriculumm525a71978336c822_1528449076687_0Core curriculum

IX. Analytic geometry on the cartesian plane. The student:

7) identifies the images of circles and polygons in axial symmetries with respect to the axis of the coordinate system, the centre symmetry (symmetry about the centre of the coordinate system).

Timingm525a71978336c822_1528449068082_0Timing

45 minutes

General objectivem525a71978336c822_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm525a71978336c822_1528449552113_0Specific objectives

1. Finding the image of the point in translation along the axis of the coordinate system.

2. Finding the image of the figure in translationimage of the figure in translationimage of the figure in translation along the axis of the coordinate system.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm525a71978336c822_1528450430307_0Learning outcomes

The student:

- finds the image of the pointimage of the pointimage of the point in translation along the axis of the coordinate system,

- finds the image of the figure in translationimage of the figure in translationimage of the figure in translation along the axis of the coordinate system.

Methodsm525a71978336c822_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm525a71978336c822_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm525a71978336c822_1528450127855_0Introduction

The teacher introduces the subject of the lesson – looking for the image of the point or a figure in translation along axes of the coordinate system.

Procedurem525a71978336c822_1528446435040_0Procedure

Task
Students work individually, using computers. Their task it to observe the way of finding the image of the pointimage of the pointimage of the point after translating along the axis X or the axis Y. They should also conclude what is the relation between the coordinates of the pointcoordinates of the pointcoordinates of the point and its image in the given translation.

[Geogebra applet]

The conclusion students should draw:

- As a result of the translation of the pointtranslation of the pointtranslation of the point A (x, y) by p units along the X axis and by q units along the Y axis we obtain the point B whose coordinates are (x + p, y + q).

Students analyse the example in groups.

Example:
In the rectangular coordinate systemrectangular coordinate systemrectangular coordinate system we mark the point A (2, 3) and translate it by 3 units to the right along the axis X and by 5 units up along the axis Y.
As a result we obtain point B:
B (2 + 3, 4 + 5) so B (5, 9).

Students use obtained information in the exercises.

Task
The point A (-4, 3) has been translated:

a) by 3 units to the right along the X axis and by 1 unit up along the Y axis,

b) by 3 units to the left along the X axis and by 1 unit down along the Y axis,

c) by 2 units to the right along the X axis and by 1 unit down along the Y axis,

d) by 5 units to the left along the X axis and by 4 units up along the Y axis.

Give coordinates of the B point that is the image of the pointimage of the pointimage of the point A in this translation.

Task
Mark in the coordinate system the point A (1, -2) and the point B being its image after the translation:

a) by 2 units to the left along the X axis and by 1 unit up along the Y axis,

b) by 4 units to the right along the X axis and by 2 units down along the Y axis,

c) by 3 units to the right along the X axis and by 3 units up along the Y axis,

d) by 6 units to the left along the X axis and by 4 units down along the Y axis.

Task
There is a triangle ABC whose vertices are A (0, -2), B (-1, 4) and C (5, 2). Find coordinates of the vertices of the triangle A’B’C’ that is an image of the ABC triangle in the translation by 2 units to the right along the X axis and by 4 units down along the Y axis. Draw the triangle ABC and its image on the coordinate system.m525a71978336c822_1527752263647_0There is a triangle ABC whose vertices are A (0, -2), B (-1, 4) and C (5, 2). Find coordinates of the vertices of the triangle A’B’C’ that is an image of the ABC triangle in the translation by 2 units to the right along the X axis and by 4 units down along the Y axis. Draw the triangle ABC and its image on the coordinate system.

Task
Prove that the tetragon ABCD is a parallelogram if: A (-3, -1), B (-4, 1), C (0, 1), D (-1, -1).m525a71978336c822_1527752256679_0Prove that the tetragon ABCD is a parallelogram if: A (-3, -1), B (-4, 1), C (0, 1), D (-1, -1).

An extra task:
Point A (4, 2) is given.
After translating the point A by 3 units to the right along the axis X and by 5 units down along the Y axis we obtain the point B. Then, by translating the point B by one unit to the left along the X axis and by 2 units down along the Y axis we obtain the point C. Calculate coordinates of points B and C.

Lesson summarym525a71978336c822_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

- As a result of the translation of the pointtranslation of the pointtranslation of the point A (x, y) by p units along the X axis and by q units along the Y axis we obtain the point B whose coordinates are (x + p, y + q).

Selected words and expressions used in the lesson plan

coordinates of the pointcoordinates of the pointcoordinates of the point

image of the figure in translationimage of the figure in translationimage of the figure in translation

image of the pointimage of the pointimage of the point

rectangular coordinate systemrectangular coordinate systemrectangular coordinate system

translation of the pointtranslation of the pointtranslation of the point