Reflect each of the shapes $A,B$ over some lines $l_A,l_B$ respectively and rotate the shape $C$ such that a $4 \times 4$ square is obtained. Identify the lines $l_A,l_B$ and the center of the rotation, and also draw the transformed versions of $A,B$ and $C$ under these operations. Proposed by Mahdi Etesamifard - Iran
Problem
Source: IGO 2024 Elementary Level - Problem 1
Tags: geometry
15.11.2024 01:34
This is what I got [asy][asy] size(200,150); // Set the size of the canvas // Define the boundary for the grid int xMax = 16; int yMax = 12; // Draw vertical line segments for (int x = 0; x <= xMax; ++x) { for (int y = 0; y < yMax; ++y) { draw((x, y)--(x, y+1), gray); // Vertical segments } } // Draw horizontal line segments for (int y = 0; y <= yMax; ++y) { for (int x = 0; x < xMax; ++x) { draw((x, y)--(x+1, y), gray); // Horizontal segments } } filldraw((1,10)--(1,11)--(5,11)--(5,10)--(4,9)--(3,10)--(3,9)--(2,9)--cycle, red); filldraw((1,10)--(2,9)--(3,9)--(3,8)--(4,8)--(4,7)--(1,7)--cycle,green); filldraw((4,7)--(5,7)--(5,10)--(4,9)--(3,10)--(3,8)--(4,8)--cycle, blue); draw((8,0)--(8,3)--(9,3)--(9,2)--(10,2)--(10,1)--(11,0)--cycle,green+1); draw((0,6)--(0,10)--(1,10)--(2,9)--(2,8)--(1,8)--(2,7)--(1,6)--cycle, red+1); draw((14,9)--(15,10)--(16,9)--(16,11)--(15,11)--(15,12)--(14,12)--cycle, blue+1); draw((11,0)--(0,11),red); draw((1,0)--(13,12), green); draw((9.5,9.5),blue+3); [/asy][/asy]
16.11.2024 14:32
Reflect each of the shapes $A,B$ over some lines $l_A,l_B$ respectively and rotate the shape $C$ such that a $4 \times 4$ square is obtained. Identify the lines $l_A,l_B$ and the center of the rotation, and also draw the transformed versions of $A,B$ and $C$ under these operations. Proposed by Mahdi Etesamifard - Iran
13.12.2024 23:40
Does somebody have any news when the official results will be published?