{"version":8,"graph":{"viewport":{"xmin":-5.7725443916234145,"ymin":-3.1640237800508855,"xmax":4.493701681546394,"ymax":3.9410816753293867}},"randomSeed":"79973ee2324d8c55cdc9e3646b0fcac8","expressions":{"list":[{"type":"expression","id":"22","color":"#c74440","latex":"a=3.9","hidden":true},{"type":"text","id":"17","text":"Transformation matrix (2x2, TL BL TR BR)"},{"type":"expression","id":"9","color":"#6042a6","latex":"m_{1}=\\left[\\cos a,\\sin a,\\cos\\left(a+\\frac{\\pi}{2}\\right),\\sin\\left(a+\\frac{\\pi}{2}\\right)\\right]"},{"type":"text","id":"15","text":"Original and transformed points"},{"type":"expression","id":"5","color":"#388c46","latex":"p_{o}=\\left[\\left(-1,-1\\right),\\left(0,-1\\right),\\left(1,-1\\right),\\left(-1,0\\right),\\left(0,0\\right),\\left(1,0\\right),\\left(-1,1\\right),\\left(0,1\\right),\\left(1,1\\right)\\right]"},{"type":"expression","id":"7","color":"#c74440","latex":"p_{f}=\\left(m_{1}\\left[1\\right]p_{o}.x+m_{1}\\left[3\\right]p_{o}.y,m_{1}\\left[2\\right]p_{o}.x+m_{1}\\left[4\\right]p_{o}.y\\right)"},{"type":"text","id":"19","text":"Select point pair"},{"type":"expression","id":"13","color":"#388c46","latex":"t=9","slider":{"hardMin":true,"hardMax":true,"min":"1","max":"9","step":"1"}},{"type":"expression","id":"12","color":"#388c46","latex":"p_{o}\\left[t\\right]","hidden":true},{"type":"expression","id":"11","color":"#c74440","latex":"p_{f}\\left[t\\right]","hidden":true},{"type":"text","id":"21","text":"Example matrices (set m_1): [1,0,0,1] = identity; [0,1,1,0] = reflection over y = x; [a,0,0,1] = dilate horizontally by a;"}]}}