document.write( "Question 1051690: Show that the points (2,-3) (5,0) (2,3) and (-1,0) are the vertices of a square \n" ); document.write( "
Algebra.Com's Answer #667183 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Use the slope formula to show that all four sides are perpendicular.\r\n" );
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document.write( "To show that the line from (-1,0) to (2,3) is perpendicular\r\n" );
document.write( "to the the line segment from (2,3) to (5,0),\r\n" );
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document.write( "1. find the slope of the line segment from \r\n" );
document.write( "(-1,0) to (2,3):\r\n" );
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document.write( "Use the slope formula:\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
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document.write( "where (x1,y1) = (-1,0)\r\n" );
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document.write( "and where (x2,y2) = (2,3)\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%28%283%29-%280%29%29%2F%28%282%29-%28-1%29%29\"\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%283-0%29%2F%282%2B1%29\"\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"3%2F3\"\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "2. find the slope of the line segment from \r\n" );
document.write( "(2,3) to (5,0):\r\n" );
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document.write( "Use the slope formula:\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
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document.write( "this time where (x1,y1) = (2,3)\r\n" );
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document.write( "and where (x2,y2) = (5,0)\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%28%280%29-%283%29%29%2F%28%285%29-%282%29%29\"\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%280-3%29%2F%285-2%29\"\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"%28-3%29%2F3\"\r\n" );
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document.write( "\"m\"\"%22%22=%22%22\"\"-1\"\r\n" );
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document.write( "3.  Point out that their slopes 1 and -1,  are \r\n" );
document.write( "opposite-signed reciprocals, or what is the\r\n" );
document.write( "same thing, their product (1)(-1) is -1.  That\r\n" );
document.write( "proves that they are perpendicular and that the\r\n" );
document.write( "angle between them is a right angle.\r\n" );
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document.write( "4.  Find the length of the line segment from \r\n" );
document.write( "(-1,0) to (2,3):\r\n" );
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document.write( "Use the distance formula:\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\r\n" );
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document.write( "where (x1,y1) = (-1,0)\r\n" );
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document.write( "and where (x2,y2) = (2,3)\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%28%28%282%29-%28-1%29%5E%22%22%29%5E2%2B%28%283%29-%280%29%5E%22%22%29%5E2%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%28%282%2B1%29%5E2%2B%283-0%29%5E2%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%28%283%29%5E2%2B%283%29%5E2%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%289%2B9%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%2818%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%289%2A2%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"3sqrt%282%29\"\r\n" );
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document.write( "5.  Find the length of the line segment from \r\n" );
document.write( "(2,3) to (5,0):\r\n" );
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document.write( "Use the distance formula:\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\r\n" );
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document.write( "this time where (x1,y1) = (2,3)\r\n" );
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document.write( "and where (x2,y2) = (5,0)\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%28%28%285%29-%282%29%5E%22%22%29%5E2%2B%28%280%29-%283%29%5E%22%22%29%5E2%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%28%285-2%29%5E2%2B%280-3%29%5E2%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%28%283%29%5E2%2B%28-3%29%5E2%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%289%2B9%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%2818%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"sqrt%289%2A2%29\"\r\n" );
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document.write( "\"d\"\"%22%22=%22%22\"\"3sqrt%282%29\"\r\n" );
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document.write( "6.  Point out that the two line segments are equal\r\n" );
document.write( "in length.\r\n" );
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document.write( "Now, using the same method, finish by showing that\r\n" );
document.write( "the slope of the line segment from (5,0) to (2,-3)\r\n" );
document.write( "is perpendicular to the line segment from (2,3) to\r\n" );
document.write( "(5,0).  Then show that those line segments are\r\n" );
document.write( "equal in length.  \r\n" );
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document.write( "Then show that the slope of the line segment from \r\n" );
document.write( "(5,0) to (2,-3) is perpendicular to the line segment \r\n" );
document.write( "from (2,-3) to (-1,0).  Then show that those line \r\n" );
document.write( "segments are equal in length.\r\n" );
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document.write( "Then point out that the line segment from (2,-3) to\r\n" );
document.write( "(-1,0) is perpendicular to the line segment from\r\n" );
document.write( "(-1,0) to (2,3), and that is has the same length.\r\n" );
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document.write( "You finish.\r\n" );
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document.write( "Edwin
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