1. (2 п) Нека је
![ABCDEF ABCDEF](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/2cc1e66318d738b7f85d162b5ea4ceec.png)
правилан шестоугао. Репер
![Axy Axy](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/efc40a872f0bc081fb1d014df4c306dd.png)
има координатне векторе
![\overrightarrow{e_1}=\overrightarrow{AB} \overrightarrow{e_1}=\overrightarrow{AB}](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/cb19160793d5e090ccf157910074f977.png)
,
![\overrightarrow{e_2}=\overrightarrow{AF} \overrightarrow{e_2}=\overrightarrow{AF}](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/66977c4031eba94c0d8491106649f7d1.png)
, а репер
![Cx'y' Cx'y'](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/8cb1810a7f5175b3d25760f837943929.png)
координатне векторе
![\overrightarrow{f_1}=\overrightarrow{CB} \overrightarrow{f_1}=\overrightarrow{CB}](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/a19df5745f731c2f126938d7a4d14878.png)
,
![\overrightarrow{f_2}=\overrightarrow{CD} \overrightarrow{f_2}=\overrightarrow{CD}](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/f90de1dd3aeaf4b7ff27785d3dcdbe8d.png)
. Одредити формуле које представљају везу координата
![(x,y) (x,y)](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/946808be8ea681a4fb565132cef2c61e.png)
и
![(x',y') (x',y')](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/7249851567017c256cf83cfc5477e993.png)
, има инверзне формуле, као и координате темена шестоугла у оба репера.
2. (2 п) Дате су координате тачака
![A(2,1) A(2,1)](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/e272faf727f8fb293e7cc54197422da0.png)
,
![B(3,0) B(3,0)](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/a4b80ad76410b7f64530610c5a3b79a8.png)
и
![C(1,4) C(1,4)](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/d248112ae2d776fbcb59ddcc95b37a65.png)
у односу на афини репер
![Oxy Oxy](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/bcc13a3b1748c2df1fcff8e56a6b2123.png)
у равни. У односу на нови афини репер
![O'x'y' O'x'y'](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/4f992e7c90afd9905cfcd03e897fd638.png)
те исте тачке имају координате
![A(1,6) A(1,6)](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/3b5fc770a45ac15e3876c40f601c5676.png)
,
![B(1,9) B(1,9)](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/86068f402ec96067a5e2d8a4797cb24a.png)
и
![C(3,1) C(3,1)](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/744ca8121294b385ae991412cf741acf.png)
. Изразити координате
![(x,y) (x,y)](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/946808be8ea681a4fb565132cef2c61e.png)
произвољне тачке
![M M](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/30e1607d7260db1196cd907a6d5a280f.png)
у реперу
![Oxy Oxy](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/bcc13a3b1748c2df1fcff8e56a6b2123.png)
помоћу координата
![(x',y') (x',y')](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/7249851567017c256cf83cfc5477e993.png)
те исте тачке у новом реперу
![O'x'y' O'x'y'](https://elearning.rcub.bg.ac.rs/moodle/filter/tex/pix.php/4f992e7c90afd9905cfcd03e897fd638.png)
.