document.write( "Question 1209028: If two vertices of an equilateral triangle are (0,0) and (0,4), find the third vertex. How many of these triangles are possible? \n" ); document.write( "

Algebra.Com's Answer #847608 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "The side connecting points A = (0,0) and B = (0,4) is vertical y-axis.\r\n" );
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document.write( "The third vertex C lies on the perpendicular to AB in its midpoint.\r\n" );
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document.write( "The midpoint of AB is  the point (0,2).\r\n" );
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document.write( "The perpendicular to AB in its midpoint is horizontal line y= 2.\r\n" );
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document.write( "The altitude of this equilateral triangle has the length   =  = .\r\n" );
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document.write( "This altitude is the distance of the third vertex C from y-axis - hence, it gives x-coordinate of vertex C.\r\n" );
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document.write( "Thus, the point C, which is the third vertex of the triangle, has coordinates  (x,y) = (+/-,).    \r\n" );
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document.write( "So, one version is when triangle ABC lies in the first quadrant. Then its third vertex is  (x,y) = (,).\r\n" );
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document.write( "Another version is when triangle ABC lies in the second quadrant. Then its third vertex is  (x,y) = (,).\r\n" );
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document.write( "So, there are two possible equilateral triangles ABC and two different positions for vertex C.\r\n" );
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\n" ); document.write( "\n" ); document.write( "All you need to know and to use to solve this problem is basic elementary properties of equilateral triangles.\r
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\n" ); document.write( "\n" ); document.write( "By knowing it and using it, you solve this problem MENTALLY in 10 or 20 seconds.\r
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