The coordinates of quadrilateral \(QUAD\) are \(Q(−6,1)\), \(U(−3,7)\), \(A(4,−2)\) and \(D(1,−8)\). In this topic you will learn about the most useful math concept for creating video game graphics: geometric transformations, specifically translations, rotations, reflections, and dilations.This fact is centrally important all over mathematics.
Translate \(\Delta DEF\) to the right 5 units and up 11 units. In particular, the hyperbolic plane is the universal cover of every Riemann surface of genus two or higher. Find the translation rule that would move \(A\) to \(A′(0,0)\), for #16.If \(\Delta A′B′C′\) was the preimage and \(\Delta ABC\) was the image, write the translation rule for #15.If \(\Delta A′B′C′\) was the preimage and \(\Delta ABC\) was the image, write the translation rule for #14.What can you say about \(\Delta ABC\) and \(\Delta A′B′C′\)? Can you say this for any translation?.Find the lengths of all the sides of \(\Delta A′B′C′\).Find the lengths of all the sides of \(\Delta ABC\).Use the triangles from #17 to answer questions 18-20. Each bar of the xylophone is based on one of the base bars.
In questions 14-17, \(\Delta A′B′C′\) is the image of \(\Delta ABC\). Some other variables are added to simplify the calculations when applying different transformations. Find the vertices of \(\Delta A′B′C′\), given the translation rules below. Use the translation \((x,y)\rightarrow (x+5, y−9)\) for questions 1-7. What if you were given the coordinates of a quadrilateral and you were asked to move that quadrilateral 3 units to the left and 2 units down? What would its new coordinates be?
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