Exam 1

  1. Question

    Given two points p=(3,4) and q=(5,2) in a Cartesian coordinate system:
    1. What is the Manhattan distance d1 (p,q)?
    2. What is the Euclidean distance d2 (p,q)?
    3. What is the maximum distance d (p,q)?

    Solution

    The distances are visualized below in green ( d1 ), red ( d2 ), and blue ( d ).
    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RSiYDfHyb+ZU6dOnXlypVr165NTEy8cOFCa2trYGAgANx7771Xrlz5+eefbWwEvEp0dxhSJcKQqj4MqRKZYki1K5bp7+8v+k1jSJUAQ6r6MKRKhCFVPuE5LITowpAqQshU4IbVA4ZUiTCkqg9DqkQYUhUVhlSJMKSqD0OqRBhS5ROGVA2DIVV9GFIlwpCqqDCkSsTIP0tgY6vSwpAqEYZURYUhVSIMqerDkCoRhlRFhSFVIgyp6sOQKhGGVEWFIVUiDKnqw5AqEYZURYUhVSJ2iqEYUiVi51DBkKqoMKRKhCFVfRhSJcKQqqgwpEqEIVV9GFIlwpCqqDCkSoQhVX0YUiXCkKqoMKRKxE4xFEOqROwcKhhSFRWGVIkwpKoPQ6pEphhSpQhDqkQYUtWHIVUikwipsgNDqkQYUtWHIVUioUOq+OZnhJB48AJ+fNKGVGlPodPVoaSusbmFkf/YFEqlQsnEK8I4jmtsZuUbxM6hIm9r115RQyC4YfWgDanSngIAoFneun7TTtpT6Gzeub+ssob2FAAA6Rnn0jPO0Z4CAKCssmbzzv20p9BZv2mnoKe6+29/ygmTi1BQ5ORgp1CoaE8BAGBhbjbcl5X3W/h4DWbkUiouTg60R9AZZG3l4zWY9hQ6w329GLnwjrurs6Bvn8JzWAgh8eA5LD5xHKg1GtpT6DDy7jBgaRINx2mY+S+WnbuFoUk0wn5/cMPqAUOqRBhS1YchVSJTDKlShCFVIgyp6sOQKhGGVPmE57AQogvPYSGETAVuWD1gSJUIQ6r6MKRKhCFVUWFIlQhDqvowpEqEIVU+YUjVMBhS1YchVSIMqYoKQ6pEjPyzBDa2Ki0MqRJhSFVUGFIlwpCqPgypEmFIVVQYUiXCkKo+DKkSYUhVVBhSJcKQqj4MqRJhSFVUGFIlYqcYiiFVInYOFQypigpDqkQYUtWHIVUi0w2pnjlz5rHHHhP5RjGkSiRESLWqqkoikWRlZT3//PO+vr4+Pj4rVqxoamrq468cOXLknbi4d+Lijh49yu8wBsCQKpHphlQrKir27Nkj8o1iSJVIuJDqsmXL5s6dm5qaWlZW9txzz913332ZmZn673Cuq6tbsGBBenq69rfbN38/bdq03bt3u7pSO7OGIVUikwipenh46H9QoVB0/6OqKjGeCGBIlUi4Yqi3t/enn34KAAEBAbt37w4LC0tMTHz00Udv+bTly5d37VZaaWlpK1as+O9//yvQYLeFIVUioUOqTGxYy5YtW7t2raur69KlS7tet1lUVLR3796lS5eKOUmzvFXe2u7FwE/EOI67fLUsyN+X9iAAAMUlN3y93c3N+D9aHn744a5fjxkzxt/f/8SJE7dsWDdu3Ni3b5/+3927d29FRYWXF53zzR2dnaU3qoX+99lPhcWlI4b7SBh4L0JFdZ3tIGt7wR7uyeLi4gRauv9mzJgRFRW1d+9etVq9du3axx57bObMmdbW1rt27Tp58uTMmTNnzpzZz6V27dr15JNP/tCLixcvTp2z2NPTw9vDrbSievOv+5paWgOGDpG3tm3cnnC15EZHR2fOpaI/z+Seyr5wT3iIRCLZte/3o8fOjAz0s7K0TDmemXTomLubs5OD/bmLl39NOiKTyXpbaszIAAD4ZnuCYUu5uTh9uyPhfH7xwJca+FTf/pR4KuuCvK2dxy/Qw9Xx888/d/MNau2ArqVOHEsbNMh64YIF3ZfavGPn4WRy7kEptZVaWPM4Vf+XSjyYvu/Icf+h3iIcDLddat/R4yMD/RzsbMU8RIlLpWdk29kO8vVy722pI+knNBKz+6dNNXCz4JhRU1MTExPj7OyckJDAcVxiYqIB4zU2Nmb1LiwsbPqsB1vbFRzHdXR2llZUNzbLOY7TaLjyypq6+sbr5ZWZuflVtTcra+q0C95saCqvrNFoNBzHNbe0llZUqzo6OI5rVyhKK6r7WEr71w1eSqnq2HvkOC9LDXyqw3+cKrhSwu8XWFlZCQD/eu+DrqUqa+o8PD1ffPHFW5Y6cfJUb0fv4d/T+J2q/0tVVNXFH0gT52C47VK/Jh1RKFUiH6LEpVKOZ14vr+xjqdg1a2LXrOEMxdCGxXGcRqP5+uuvLS0tV65c+dNPP/G+n0ZGRkZGRvK7JjKMdsMaN25cZ2en9iMHDhwAgF9++eWWz+zs7PTx8dHfrXzd3NRqteiDowGJjY2NjY01+K+z9bIGiUTywgsvZGZmnjx58plnnhF/AAypEgkXUi0sLHzwwQd37Njx4YcfLly4MCwsbOHChbd8jkwm+/bbb/X/7rcNDVLSuS1xcBhSJTHFkGpoaGhmZmZsbOwrr7wi8k1jSJVIuJDqDz/84Onp+frrr2/cuHHBggVpaWnEq2XMmTMnLy/voUceAh8AH3hofkzenDkPdnbCwoVA6QeFGFIlMtGQqrW19VtvvSX+7WJIlUi4kKqdnd3WrVv785mjR4/+Zc8vtmALAL/Ar4PUVrBsGfz8MyxcCLt3w7x5QozXBwypEgkdUmXii2RHsL9fsL8f7SkAAKwsLZ9aOIf2FDoL57LyLt//J5PBtm0AQGvPcnFyYOduYedQmfaXsYKuz+JTQoowpErEziQ9aPesv/4VVCoqzw3ZuVsYmgRDqmLCkCqRECFVDw8PjuPmzh3YJXTo7VkYUiUSOqSKG1YPGFIlYiekSkBpz8KQKhGGVPmEIVWj1gqt2pPucpAPgp5v/lCrdefgLSyonINH/YQhVYTon89C4sANqwcMqRKxE1Lti7h7FoZUiYQOqeKG1QOGVInYCanehoh7FoZUiRoam1uEfAkrnsPqAUOqRIyEVPs6h9WdKOezMKRKJHRIFR9h9SCTyRjZrYClOuYga/q71R0Q5XEWhlSJrCwtBE0R44bVA4ZUidgJqfaX8HsWhlSJMKQqKgypErETUr0DAu9ZGFIlwpCqqDCkSsROSPXOCPl+QwypEgkdUsVHWD3Y2lgLXYLsJ9ZCqoKemBCQYI+zWAupMnKScbCLk6ApYtywesCQKhE7IVVDCLNnYUiVyHRDqlRgSJVIiJCqqATYszCkSiR0SBU3rB6ChvtOjBhFewoAkwmpiofvPQtDqkQTI0YFDRewTYcbVg+uzo6MlOZYC6laWVrSnmLAeN2zWAupMnKVEX8/b0FTxEx8kexolrcy8oYYjuMKi0tpT6FTXHKjo1PAsoB4+NuzOjo7i0tu8DjaQBQWlzLylpWK6jpBry6PG1YPFwquMnJioqmldUfCIdpT6CQcTK+oYmIf5wFPe1ZFVV3CwXReJzPcjoRDTS1MRCjSM7IvFFwVbn3csHrw9nQbIeQz8P6zsbaaxMbZNACIGDXC2dGe9hT84WPPcna0jxg1gvfRDDMpYpSgr37qvxHDfb093YRbH9/8jIxGf9/83E94zT8a8M3PfMKQKpFwIVWaBvY4C0OqRKYYUqUIQ6pEwoVUKRvAnoUhVSKhQ6q4YfXg5GDn7srEC45MJKRKn6F7FoZUiYQOqeI5LGQ0eD6H1R2ezxILnsPiE4ZUidiZRCgGPc5i525haBIMqYoJQ6pEQoRUmXOHexaGVIkwpCoqDKkSMR1S5dGd7FkYUiXCkCqf8ByWURPwHFZ3eD5LSHgOCyFeYZOVYbhh9YAhVSLjCKnyqB97FoZUiTCkKioMqRIZTUiVR7fbszCkSoQhVT5hSNUwRhZS5VHv57MwpEqEIVVRYUiVyMhCqjzq/XEWhlSJMKQqKgypEhlfSJVHvexZGFIlwpCqqDCkSmSUIVUekfYsDKkSCR1SJW9YEydO/Oabb27eFPCG9XEcp1KptL9WKBQJCQn/+c9/MjMzxTzLNmZkwPSo8aLdXB9YC6kOEfKqbEZAb8/CkCrR9KjxY0YGCLc+ecNycXFZtWqVp6fnI488kpSU1LWPCEShUKxatcrBwcHBwWHJkiVyuTwyMvLRRx9duXLlhAkT5s+f394u0tsOMKRKZMQhVR713LNk+/djSFUfnZBqcnJyRUXF559/XlFRMX/+fE9PzxdeeEG4Bzuffvrpxo0bFy1a9M4775w9ezYqKqqysvLIkSOlpaVbt25NSUlZt26dELerD0OqRMYdUuVRzz2r6N8baQ+kYzohVVlcXBzxDwYNGjRx4sSnn376iSeesLGxSUxM/PTTT3fu3NnS0jJ06FAHBwceh1i5cuXy5cu//vrre++9NyIi4uOPP/7kk08WL17s4OAQHh7e3t6+Z8+ef/zjH/1ZKisr66uvvkrpxZ9//hkUNmnChHucHOwam1tSjmcpVR3urs6qjo4jx87U1jfWNzYXXCmpqWu4cr18uK+XRCI5k3Mp99IVH6/BZmZml4qunT53ydnJwcbaqqyi+s/Tuebm5r0t5ePlDgC/H88ybCkrK4vt8clKVcfAlxr4VDsSDlZU10lAwuMXaMBS5tbSj+AjAHi8fPlge2ch7vbbL1Vw1ee5lWYlJZCT43j0iNw/0HJMqNAHw22XSjz0R/ioAFsbGzEPUeJSx07n2Fhb+np79LZUStoxTiKdfl+0YXvFbU66q1Sqy5cvl5SUaM9nyWSyDz/8MDAwcP369YbdHlF5efn48bozR6GhoQAQEhLS9aehoaFXrwrY4eiOqZDqnPujaE+hM2ViODs/OKdPJoNt2xrmxsjUnfbLn2ThvTsjhvvaDrKhPQUAwBDPwYKGVIEjaW9v37t379/+9jftI6nRo0e/9957BQUFHMc1NzdrX/qVn59P/LsGCAwMXLNmjfbXGo3mt99+q62t7frT999/f9iwYbzcUGRkZGRkJC9LIfHJOTlwABzIOTntWTius5P76185AM7CgktKoj2N0YiNjY2NjTX4r5MfYbm5uT300ENZWVkvvfTSpUuX8vLy3n777aCgIACws7N74403AKC4uJivTXPx4sXr1q1bs2bN8ePHJRLJY4895urqCgCNjY27du367LPPZs+ezddt9Q1DqkR3T0iVPx0cV/zeR4y8R9rUQ6ovv/zyhQsXLl68+O67744ceWsw3drauqysbObMmXwN8dZbbz399NOffPLJ6tWru388Ojp68eLF48aNe++99/i6rb5hSJXorgqp8qSiqi7hyJ+MXNfBdEKq5AvX/+tf/+rj78hksiFDhvA4hJWV1YYNGz777LOqqqruH3/33XeHDBkyfvx4iVg/s/X2dLOwMBfntvqGIVXG6UKq2p8bAsDPP8PChbSun8VUSNXNxVG49fHNz8hoUHjzcz/hNf/6Dd/8zCcMqRLdnSHVgeG6h1RpX/OPnUMFQ6qiwpAq0V0bUh2AW0OqVPcsDKmaKAypEt3NIVVDEUKq9PYsDKnenfAcllFj9xxWd3g+q094DotPGFIlYmcSppDvFhqPs9j5BmFIVVQYUiUyiZDqHeorpCr6noUhVROFIVUiUwmp3onbhFTF3bMwpHp3wnNYRs04zmF1h+ez9OA5LIRYRfv1WXcf3LB6wJAqkcmFVPuhvyFVUfYsDKmaKAypEpliSPV27iCkKvyehSHVuxOGVA1juiHV3t1xSFXI81nsHCoYUhUVhlSJTDek2rs7DqkK+TiLnUMFQ6qiwpAqkUmHVHthSEhVsD0LQ6omCkOqRKYeUiUxMKQqzJ5lOiFVJt4wyY4xIwMChvJ5bUKDsRZS9XZ3pT0FWwwPqQpwzT+mQqqCXkoQH2H1gCFVIgyp6pPJZIaHVPl+nGXqIVWThSFVIgyp6mtTKDNz8w3/+7zuWaYTUsUNq4cr18uz8wppTwEA0NLadjDtDs/pCiY9I7u/rzkyGTV19QPtlfC3Zx1My2hpbRvQMDzJziu8cr1cuPVxw+qBqZDqvFlTaE+hM3PKBA83Jq5ryA4PN+eZUyYMdBWe9qx5s6bY2TLx5sqJEaMEDanihtWDq7Ojv5837SkAAGRS6T1htwbWaAkLCbSytKQ9BVusLC3DQgJ5WIiPPeuesJGMXGXE38/b1VnAag4TXyQ7MKRKhCFVfR2dncUlN/hZa8B7lqmHVE0WhlSJMKSqr6KqLuFgOm/LDWzPMp2QKng7L6gAAB0ESURBVG5YPXh7uo0Q8hl4/2FIlXG6kCqPBrBnMRVS9fZ0E259fPMzMhpMvflZKHf7Nf/wzc98wpAqEYZU9fUIqfLIoMdZ7BwqGFIVFYZUiTCkqu/WkCqP7nzPwpCqicKQKhGGVPURQqo8usM9C0Oqdyc8h2XUTOIcVnd34/ksPIfFJwypErEzCVMEv1v6/TiLnW8QhlRFhSFVIgyp6usrpMqj/u1ZGFI1URhSJcKQqr7bhFR51I89C0Oqdyc8h2XUTO4cVnd3y/ksPIeFkAnAJisA4IZ1CwypEmFIVV9/Q6o86n3PwpCqicKQKhGGVPXdQUiVR73sWaYTUgWODSqVKjEx8aOPPtq1a5dSqez+R9nZ2V988QUvtxIZGRkZGdnHJ3R2drYrlH18gpjkrW20R9CRt7VrNLSH4Dg5JwcOgAM5J6c9C6fRcPK2djq33dnJ/fWvHIDawmLT889PmDDB2dk5LCwsLi6utbW1t7+kUqneeuutESNGODk5zZo1KzMzUyaTpaWl8Ttau0LZ2dnZxyfExsbGxsYavD4Tr46tr6+fOXPm2bNntb8NDg4+dOiQn5+f9rd//PHHSy+99M9//lOESWSyvqK1ImOnjokvc9d3xyFVHslksG0bB/DYzz8nbtyo/Vh9fX1ubm5CQsKJEydsbQkFnWXLlu3evXvVqlVjxow5cODA5MmThXj1ltAdYiaeEr799ttFRUV79+5tbm5OTk5uaGh45JFHVCqV+JNgSJUIQ6r6DAmp8kgm279ggf45zvPnz3/55Zf6n56Tk/Prr79++eWX69evf/LJJ3fv3h0TEyPEXEKHVJl4hJWcnPzaa69p78HZs2drt/+NGze+9NJLd7pUU1PTlStXevtTuVzu6uHdplDaWFl2qtWVNTftbQc52A3iOKiorrWytKisuVlSXjXM14vjOA83FwCob2xuVyi93F0lEkmLvK2xRe7h5mxuZqZQKmvrm1ycHHpbysXJAQCq6+oNW4rjuHMXLk8aO2rgSw18qotFV11dHIOG+/L4BRqwVNfR+qBmjoXUnOM4parDzExmJpMBgFKlkkqk5uZmAKDq6AAOLCzMAaCjs1Oj0VhaWACAWq3u6FRbWphLJBKNRqPq6DQ3N5NJpQYs1SprrwlsXM95DHwpw6YqSi4iHuRJSf99Y/XqW+72Y8eOSaXSBYuWAADHQUV13cJFixMTE3n/Dl4quq7huGE+Xr0tBQPrkTGxYdXU1AQEBHT9dty4catWrXr//fefeOIJV9c763ceOnRo3bp1vf1pcXHxuKlzLxQUTwgPqaiui9+fGjJi2APRk1rb2nbvTx3s4jhv1pSAoUPiD6Sp1ernn3xMKpEc/TOzoqr2qUVzHO3tTudcPH/pysMPTBnu651/pSTtxNmoCWG9LfXX+bMAYE9yumFLzZo66fGH7+dlqYFPNXXS2D9PnatvaOLxCzRgKV9fd2uNTbu07Zj0DwAACUD3C813fy5i3u3X3Y9xGUDXM35pt79uwFI2ADZQDBd5WMqwqXq5okx5RWVZRfUtd/vF/EKbQbbnLhY9EO2ivduVct2Pffn9DiqUytHB/gDQ21KdkgE9Z2TihaNjxoyJiIjYps3hAgBAc3Pz6NGjQ0JCkpOTv/rqq5deeomXOfGFo8Zu+9mLR8ov0Z6CCed/3Z23K17/4/PmzUtKSrrlg+vWrVu9enVbW5vl/8VEjhw5MmvWrLS0tOjoaKFH7W6ALxxl4hHWqlWrVq5cWVdXFxMT8/jjj9vb29vb22/dunXWrFkxMTFubgJecfUW1XX1DU0twf5+ot1ib9Rq9ansi5H3jKE9CABAZm7+qKDhNlaUwzkaDTwTGaJUsnLlaNrGARA2rL///e+ETx03TqPRbNmy5dlnn9V+ZPv27ULMVFBcIug1mpjYsJYvX97R0fHBBx8kJydHRUWNHj0aAO67777k5OSnn366tFS8eMyV6+Ul5VUsbFjakCojG1Z6Rrabi+PQIZ50x5BK4W8rSvIv2nkOdqE7CQC0tivKK2qC/CkWAIbfuJF49uzflcr/v7biZ599Nnv2bP1PnTZtWnR09Isvvnj9+vUxY8YcOnTo4MGDQsyUnVfoN8TjLt+wpFLpc88999xzz9XX19vY2HR9fMaMGVevXj158mQf59H5FTTcV3v2kToMqRK9+/YgAI23B+05ABRKSWGxMiyE7hQPNzRMTUxMPJ5xZlzEmDkPPjh06FDi50kkkn379r3++uu//vrrpk2bIiMjk5KSpkzh/wCbGDHKwU7At3kycQ5LNHgOCyGtK1euBAYGGt05LCZeh8UODKkSsRNSratvZORdjXyGVAcMQ6omCkOqROyEVM/k5J/Jyac9BQDvIdWBMZ2QKhPnsNjh7emmfV0fdRhSJRrmS/nEfxf+Q6oDYEBI1d/f//z58+7u7vxOMmK4r5uLI79rdofnsBBC4sFzWHzCkCoROyFVhVKpUDJxoRtOoJCqQdg5VDCkKioMqRKxE1JNzziXnnGO9hQAgoZU75zphFTxHFYPTg52CgWFq0Tow5AqkfZNtiwQNqR6hzCkenfCc1gI0YXnsPiEIVUidibRcJywoc47wc7dwtAkGFIVE4ZUidgJqaaeyEo9kUV7CgDRQqr9YzohVSae97IDQ6pE7IRUpWx8d0DMkGo/YEj17oTnsBCiC89hIYRMBW5YPWBIlYidkOqp7AuMVEIohFR7ZzohVTyH1QOGVInYCak2NrMS76ETUu0FUyFVe1ub23+eofAcVg/afonQbbV+am1rZyRN2NqusLGyGljuhB/at32w8CJJjoM2hYKR19Oyc6golCpzs77innfDNd3ZgSFVIkb+WQIbW5UWzZCqHnYOFZMIqbIDQ6pE7IRULxRevVAo4OWW+o9ySLWnPcnpqo4O2lMACB9SxQ2rh8qam9fKKmlPAQDQ1q48d/Ey7Sl0LhVda2xiYsMqq6guq6imPQUAQGOT/FKRgGeX78i5i5fb2pk4yXitrLKy5qZw67PyAJsRY0YGBAwdQnsKAAAHO9sVi+fSnkJnYcx0b/c7K9oKZNLY0bRH0Bni6bYwZjrtKXRWLJ7rYGdLewoAgOlR4+/0UoJ3BDesHmxtrG3ZOB0gkcAwH1au1uDrxfN1KQ0m6JUA7ohMJmPnbmHnUBns4iTo+viUsIfquvqC4hLaUwAAqNXqE5nnaU+hk5mb38bGyxpKyqtKyqtoTwEA0KZQZuYycXV5ADiReZ6R9z8XFJdUC/lqD9ywerhyvTw7r5D2FAD/F1KlPYVOekY2I685unj5mqCvS+y/mrp6RnolAHAwLaOltY32FAAA2XmFV66XC7c+PiXsAUOqROyEVMNCAmiPoOPh5jxzygTaU+jMmzXFzlbAfGn/CR1SxQ2rB1dnR1dnAZsf/SeTSu8JG0l7Cp2wkEDaI+h4e7jRHkHHytKSnbuFnUPF389b0PXxKWEPGFIlwpCqPgypEmFIVVQYUiXCkKo+DKkSYUhVVBhSJcKQqj5jD6kKBEOqfMIL+CFEF17Aj08YUiXCkKo+DKkSYUhVVBhSJcKQqj4MqRJhSFVUGFIlwpCqPgypEmFIlU94DgshuvAcFp8wpErEziQYUiViaBIMqYoJQ6pEGFLVhyFVIgypigpDqkQYUtWHIVUiDKnyCc9hIUQXnsNCCJkK3LB6wJAqEYZU9WFIlcgkQqqTJk267eecOnVKhEkwpEqEIVV9GFIlEjqkKouLixNu9X6ytLRMTU3Nycmxt7f38/OzJVm8eHF/lvrxxx+nT5/+aS+uXr069/Hn7Ozs/Lw9rpVVfvbdz00t8pGBQ1ta2z7495bCq6UPzYgKHO677ruf006evXdiuEQi2bxzX8LBPyJGj7C2stx39Pj2+GQfr8EuTg6nz138dnuChYV5b0tpL1H08Ybthi0VPiowZMSwTzfuGPhSA5/KwcF+y859/H6Bhi1VXdfw+5+Zwt3t/V/q2Kmcy1dLfbzcRTgYbrtUfWPzpLGjRT5EiUtV19Uveuh+mVTa21JH0k9qJGb3TzP04pQcG2pra62srD7++OMBrqNUKot7N378+GnTZ3R0dnIcp9FwdQ1NCqVS+xcbmlpa29q1v26Wtza3tGp/3dquqG9s1i2uUtU1NGk0Go7jOjs76+obcSlcCpe6o6ViY2NjY2M5QzH0U8Lo6OgHHnhg9erVwt3EbX9KeK2sorq2noWWlKqjY9/RE48+GE17EACA5NSMyHtCWQhJaSuqo4OG0x4EmlrkJzLzHrxvMu1BAAD2JKfHzIi0MKd/ZaRT2Rfc3Zz7qPjcPT8l/Pzzzx955BG6M2BIlQhDqvowpEpkQiHVcePG0R4BQ6pkGFLVhyFVIgypigpDqkTsFEMxpErEzqGCIVVRYUiVCEOq+jCkSoQhVVFhSJUIQ6r6MKRKhCFVUWFIlQhDqvowpEqEIVVRYUiViJ1iKIZUidg5VDCkKioMqRJhSFUfhlSJMKQqKgypEmFIVR+GVIkwpCoqDKkSYUhVH4ZUiTCkyie8gB9CdN09b81hAYZUiTCkqo/DkCoJhlRFhSFVIgyp6sOQKhGGVEWFIVUiDKnqw5AqEYZU+YTnsBCiC89h8QlDqkTsTIIhVSKGJsGQqpgwpEqEIVV9GFIlwpCqqDCkSoQhVX0YUiXCkCqf8BwWQnThOSyEkKnADasHDKkSYUhVH4ZUiUwipMoODKkSYUhVH4ZUiYQOqeI5rB7UanVHp9rK0kLEoXrV2tY+iI0LzLe2K2ysrCQMnNfVvu2DhRdJchy0KRSMvJ6WnUNFoVSZm8lkMllvnzDAc1j0v/FMkcn6uq9FxsghCACM/LMENrYqLYmEobuFnUNF6P/s8RxWD9fKKhg5RaLq6NiTnE57Cp3k1IymFiaei10ovKptqVLX1CJPTmXlovt7ktNVHR20pwAAOJV94VpZhXDr44bVA4ZUiTCkqg9DqkQmFFJlAYZUiTCkqg9DqkQYUhUVhlSJ2CmGYkiViJ1DBUOqosKQKhGGVPVhSJUIQ6qiwpAqEYZU9WFIlQhDqqLCkCoRhlT1YUiVCEOqosKQKhE7xVAMqRKxc6hgSFVUGFIlwpCqPgypEmFIVVQYUiXCkKo+DKkSYUhVVBhSJcKQqj4MqRJhSJVPeAE/hOjCC/jxCUOqRBhS1YchVSIMqYoKQ6pEGFLVhyFVIgypigpDqkQYUtWHIVUiEwqpchyXm5tbWlpaXV3d0dHh5eXl6+sbHh7OYygFz2EhRNddcgG/rVu3fvzxx5cv33pBlcDAwNjY2GXLlokzBseBhtMwUvpSq9WMXE2QnUm0lU4pCxc/ZeluYWgSjUYqEfD7w8S/zK1btz711FNBQUG7d+++dOlSdXV1dXV1QUFBUlLShAkTnnzyyR07REqKYkiVCEOq+jCkSmQSIdUNGzY88cQT27Ztk3TbmQcPHhwUFDRv3jxvb++vv/76iSeeEGESDKkSYUhVH4ZUiYQOqcri4uKEW72fXn311WeffXbs2LHEP9VoNN99992bb77Zn6XS0tI++eST/b04derU6AlTQ0NDXZ0da242HEg92dqm8PZwa1cokw4fq6yui7xnzMiAof898md+0fUgfz+JRJKekZ2Zm+83xMPC3Dw7r/DPzFxnR3u7QTZXrpenHM+UyWS9LTXczxsADF5qmI/X+DHBvCw18KmG+nj+ceocv1+gYUup1ZrikhvC3e39X+ry1TKlSiXOwXDbpawsLAKG+Yh8iBKX4jguevLYPpZKST/OSWTTp001bK9g4hFWeHj4b7/9tnTpUguLW69gr9Fofvnll/Dw8H4uNWTIkHHjxvX2p4WFhfY2Vo72dqD9KY+nu5uLEwCYm5v5eLnbDdLliXy93NUajfaJuMdgFytLC0sLcwBwdXZQqjq0F/x3sLf18XTHpXApXOqOlgJuQNftYuKnhEePHp07d+6IESMWLVoUGhrq7OwMAA0NDfn5+fHx8bm5uQcOHJgxY8bAb+i2P6G4ePnajapaFi4b0q5QbotPfnbpfNqDAAD8lHD4geiJLFzHQpsIYeFCyXX1jYfSTy99ZBbtQQAAvvspcdljD1pbWdIeBI4cO+Pt4TZqxLDePuFu+CnhjBkzjh49+tlnn7377rsajabr41KpdPbs2UePHp061cAHkHcKQ6pEGFLVhyFVItMKqba0tNy4caOqqorjOA8PD29vb3t7Pt9ze9vdHUOqRBhS1YchVSLTCqna2dkFBwcHBwfTGgBDqkSM/LMENrYqLQypEmFIVVQYUiXCkKo+DKkSYUhVVBhSJcKQqj4MqRJhSFVUGFIlwpCqPgypEmFIVVQYUiVipxiKIVUidg4VDKmKCkOqRBhS1YchVSKhQ6om9wgrNTV19erVvf1pTVN7q6KztIB+h8LCyjp08qxXV/2d9iAAACET7792Kau9hX6uxmPoSACouk5/p7C2cxwWMn7V6RTagwAAjJv28Fuv/1OloP/+Z9/gsbbW5m72vT4rPHbs2H333Wfw+my9DktoWVlZ8fHxfXzC2XO5ldW1dtb0OxSqjg4VZ27LxAvCQK7UyDiVtRX9n+LL21UAYGtN/35pVyjUEgtbSyaeo8hVYCHpsDCnf9y2tHd4uruNiwjr7ROkUumCBQsiIiIMvAEOdfPNN98sW7aM9hQcx3GlpaUuLi60p9AJCws7efIk7Sk4juNiY2NjY2NpT8FxHHfy5MmwsDDaU+i4uLiUlpbSnoLjOG7ZsmXffPONcOsz8f8DQgj1B25YCCGjgRsWQsho4IaFEDIauGEhhIwGblgIIaOBGxZCyGjghoUQMhpMVHPY4eTkFBAQ4OfnR3sQsLGx8fb2Dgvr9RXDYnJ1dZ00aZIVA690d3JyCgkJ8fT0pD0I2NvbDxkyJCQkhPYgAAAeHh6TJ09m4dqTzs7O4eHh2iyDEEzrrTkIIaOGTwkRQkYDNyyEkNHADQshZDRww0IIGQ3csBBCRgM3LISQ0cANCyFkNHDDQggZDdywEEJGAzcshJDRwA0LIWQ0cMNCCBkN3LD+X0pKSnR0tIODw4QJE7Zv3057HNixY8ekSZMoDqDRaH788cfw8HBbW9vhw4e/8MIL9fUCRn37plAo4uLigoODbWxsRowY8f777ysUClrDdHnjjTc8PDxo3Xp6erqkJ0dHR1rDVFRULF26dMiQIZ6env/4xz+am5uFuBWTKz/35tixY3PmzJk2bdr69evT09O1dcJly5bRmqeuru7TTz+1tbWlNQAA/PDDD88999zSpUvfeOONoqKizz///PTp0ydPnjSnEex87bXXNm3a9Oqrr4aGhmZmZsbFxdXW1n711VfiT9IlJSVl3bp1gwcPpjVAUVGRTCb7+OOPJRKJ9iOWlpZUJqmqqpoyZYqVldWbb77Z2Nj44Ycf1tfX79y5k/9bEi55aFxiYmJGjx6tVCo5jtNoNDExMUFBQRqNRvxJsrKypk2bZm1tDQATJ04Uf4Au3t7eDz74YNdv9+7dCwBJSUniT9Le3i6TybonVJ9++ml7e3sq3yCt2tpaT09PV1dXd3d3WjO89tprI0aMoHXr3cXGxrq6ulZVVWl/u3r1agCoqKjg/YbwKSEAQEtLS3Jy8qJFiywsLABAIpE88cQThYWF58+fF38YOzu7mTNnvvPOOyNHjhT/1rs0NDTcuHEjJiam6yPR0dEAcOnSJfGHqaqqmjRp0gMPPND1keHDh6tUqo6ODvGHAQCO45YvXx4cHLx06VIqA2gVFRUFBwfX1tamp6cXFBSo1WoqY6jV6i1btixZssTd3V37kbfeeisjI8PGxob328KnhAAAN27cUKvVoaGhXR8ZPXo0AJSUlIh/zc8RI0Zo/4M6depUVVWVyLfexcbGJi8vz9fXt+sjx48fBwB/f3/xhxk6dKj21jmOk8vl58+f37Jly8MPP6z9D0Z8GzduPHHiRG5u7pdffkllAK2ioqKWlhYfHx+lUgkAwcHBP/3007hx40Qeo6ampqKiYvLkySqVKjc318zMLCQkRKDTr/gICwBAuy90v66ri4sLAFRXV1ObiTZLS8vRo0fb29trf3v27NmnnnoqKCjo4YcfpjjVnj177O3to6KiBg0atGnTJioz5OXlvfrqq5s2bRoyZAiVAbQ0Gk1xcbFEIjl8+HBTU1NaWppKpZo/f75cLhd5Eu0/n/z8fE9PzwkTJowdO3bYsGGHDh0S4rZwwwIA4Hq5TjStZxxMaW5ufu211yZPnuzl5XXo0CFaD2q0oqOjU1NTv/766+rq6qlTp2ofWYipvb19yZIlf/vb3x555BGRb/oWHMedO3cuJydn6tSp9vb20dHRP/zwQ1lZ2f79+0WepLa2FgC+/PLL77//vqmpqaCgIDg4eOHChWVlZbzfFm5YAADan0w3NDR0fUT7ay8vL2ozsSE9PT00NHTz5s2ffPLJqVOnhg4dSnceV1fXadOmvfDCC1u3bs3Ozj5w4IDIA3zxxRfXrl2bOnVqUlJSUlJSUVGRQqFISko6c+aMyJPIZLLg4ODur2OIioqSSCQFBQUiT6KdYfXq1Y899pi9vX1QUNDmzZu154V5vy3csAAAvL29pVJp9++09tc+Pj70hqIvJSVl5syZI0eOvHz58ssvv0zxsVViYmJ4eHhTU1PXR7Q/kRD/dWH19fVtbW1Lly6dP3/+/Pnz9+7d29TUNH/+/LVr14o8SXFx8datW7s/AVSpVBzHdZ35Fo23tzcAdP/PzMfHRyqV1tTU8H5buGEBANjb28+ePTs+Pl6j0Wg/8ttvvwUEBERERNAdjCK1Wv3000/ff//9ycnJrq6udIcZMmRIbm7u4cOHuz6SlpYGAGPGjBF5ks8++6z7T9lfeeUV7csa4uPjRZ4EAJ566qnur3BOSEgAAPFfbOzl5RUeHr5v376uj6SkpGg0mrFjx/J+W/hTQp3XXnttxowZy5cvf/zxx1NTU3/++ecff/xRKjXdDT0jI6OkpCQ6OvqWF2dOnTpV/H18/Pjx06ZNe+aZZ4qKigIDAy9cuLB+/fqYmJh77rlH5EnY4e/vv2TJkldeeaWqqmrUqFE5OTlffPHFihUrxP/uSCSSNWvWLFiwAABiYmJKSkrWrl07derU2bNn839jvL+yy3gdPnw4KirKzs5u/Pjx27Ztoz0ON2/ePIovHN2yZQvxgPniiy+ozFNXV/fss8/6+vpaWVmFhITExcW1trZSmaS7rkdYVMjl8jfeeEN7n4SGhq5bt66zs5PWMImJiX/5y19sbW0DAgJeffVVuVwuxK1gSBUhZDRM9ykPQsjo4IaFEDIauGEhhIwGblgIIaOBGxZCyGjghoUQMhq4YSGEjAZuWAgho4EbFkLIaOCGhRAyGrhhIYSMBm5YCCGjgRsWQsho4IaFEDIauGEhhIwGblgIIaOBGxZCyGjghoUQMhq4YSGEjAZuWAgho4EbFkLIaOCGhRAyGrhhIYSMBm5YCCGjgRsWQsho4IaFEDIauGEhhIwGblgIIaOBGxZCyGjghoUQMhq4YSEjcOzYMYlE8ssvv2h/e/XqVRsbm3Xr1tGdColPwnEc7RkQur0XX3xx586d+fn5Li4uM2bMaG1tPX78uEwmoz0XEhVuWMg4yOXy0NDQe++9Nzo6+vnnn8/JyQkKCqI9FBIbbljIaKSmpk6fPt3GxubDDz/85z//SXscRAFuWMhocBwXERGRn59fVVXl5OREexxEAZ50R0Zjx44dhYWFTk5Oq1evpj0LogMfYSHjcOPGjVGjRr355puBgYGPPvpoamrqtGnTaA+FxIYbFjICHMfNmTOnsrLyzJkzZmZm8+fPz8vLy8vLs7GxoT0aEhU+JURGYMuWLYcPH968ebO5ublEItmwYUNtbe3bb79Ney4kNnyEhRAyGvgICyFkNHDDQggZDdywEEJG438BnzDVjsy4BwQAAAAASUVORK5CYII=

    1. d1 (p,q)= i | pi - qi |=|3-5|+|4-2|=4.
    2. d2 (p,q)= i ( pi - qi )2 =(3-5 )2 +(4-2 )2 =2.828.
    3. d (p,q)= maxi | pi - qi |=max(|3-5|,|4-2|)=2.