Translating a point in the coordinate system
Przesunięcie punktu w układzie współrzędnych
Learning objectives
Finding the image of the point in translation along the axis of the coordinate system.
Finding the image of the figure in translation along the axis of the coordinate system.
Learning effect
You find the image of the point in translation along the axis of the coordinate system.
You find the image of the figure in translation along the axis of the coordinate system.
Your task it to observe the way of finding the image of the pointimage of the point after translating along the axis X or the axis Y. Also decide what is the relation between the coordinates of the pointcoordinates of the point and its image in the given translation.
Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/DmdnuCKHW
The conclusion:
As a result of the translation 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).
Analyse the example.
In the rectangular 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).
Use obtained information in the exercises.
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 point A in this translation.
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.
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.
Prove 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.
Do the revision exercises.
Exercises
After translating the point D (-4, 7) by 3 units to the left along the X axis and by 1 units down along the Y axis we obtain the point D’ whose coordinates are
- (-1, 8).
- (-1, 6).
- (-7, 6).
- (-7, 8).
The point X’ (-2, 1) is the image of the point X (3, -6) in the translation
- by 5 units to the left along the X axis and 5 units up along the Y axis.
- by 1 units to the left along the X axis and 5 units up along the Y axis.
- by 5 units to the left along the X axis and 7 units up along the Y axis.
- by 6 units to the right along the X axis and 7 units down along the Y axis.
There is the line segment AB in which A (2, 4) and B (0, -2). By how many units along the X axis and along the Y axis do we need to move the point A to obtain the point that is the midpoint of the line segment AB? What are coordinates of the midpoint of the AB line segment?
Describe the solution in English.
Indicate which pairs of expressions or words are translated correctly.
- przesunięcie punktu - translation of the point
- obraz punktu - image of the point
- obraz figury płaskiej w przesunięciu - image of the figure in translation
- prostokątny układ współrzędnych - translation of the point
- współrzędne punktu - image of the figure in translation
- współrzędne punktu - coordinates of the point
- translation of the point
- prostokątny układ współrzędnych
- image of the figure in translation
- współrzędne punktu
- obraz figury płaskiej w przesunięciu
- przesunięcie punktu
- rectangle coordinate system
- coordinates of the point
Glossary
współrzędne punktu
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: coordinates of the point
obraz figury płaskiej w przesunięciu
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: image of the figure in translation
obraz punktu
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: image of the point
prostokątny układ współrzędnych
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: rectangular coordinate system
przesunięcie punktu
Nagranie dostępne na portalu epodreczniki.pl
wymowa w języku angielskim: translation of the point
Keywords
coordinates of the pointcoordinates of the point
image of the figure in translationimage of the figure in translation
image of the pointimage of the point
rectangular coordinate systemrectangular coordinate system
translation of the pointtranslation of the point