document.write( "Question 1203533: A triangle has the coordinates (2, 7), (3, 5) and (1,0)\r
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Algebra.Com's Answer #839180 by ikleyn(53765) $\"\"$ $\"About$

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\n" ); document.write( "A triangle has the coordinates (2, 7), (3, 5) and (1,0).\r
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document.write( "Let the points be A= (2,7),  B= (3,5), C= (1,0).\r\n" );
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document.write( "Then the three vectors are\r\n" );
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document.write( "    AB = (3-2,5-7) = (1,-2)\r\n" );
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document.write( "    AC = (1-2,0-7) = (-1,-7)\r\n" );
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document.write( "    BC = (1-3,0-5) = (-2,-5)\r\n" );
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document.write( "The trianle is right-angled if and only if one of the three scalar product of these three vectors is zero.\r\n" );
document.write( "So, calculate the scalar products\r\n" );
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document.write( "    AB * AC = 1*(-1) + (-2)*(-7) = -1 + 14 = 13;\r\n" );
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document.write( "    AB * BC = 1*(-2) + (-2)*(-5) = -2 + 10 = -8;\r\n" );
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document.write( "    AC * BC = (-1)*(-2) + (-7)*(-5) = 2 + 35 = 37.\r\n" );
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document.write( "As you see, no one scalar product is zero - so we conclude that the triangle is not a right-angled triangle.\r\n" );
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