document.write( "Question 1153817: A line in the coordinate plane has a slope of 4, and a distance of 1 unit from the origin. Find the area of the triangle determined by the line and the coordinate axes \n" ); document.write( "

Algebra.Com's Answer #776122 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The solution by @MathLover1 is NOT CORRECT, since it DOES NOT SATISFY the condition \r
\n" ); document.write( "\n" ); document.write( "            that the distance from the origin to the hypotenuse is 1 unit.\r
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\n" ); document.write( "\n" ); document.write( "            For the correct solution, see my post below.\r
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document.write( "Let consider this right angled triangle with vertices (0,-4), (0.0), and (1,0).\r\n" );
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document.write( "Its legs have the length 4 and 1; its hypotenuse is   =  long.\r\n" );
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document.write( "We can easy find the height \"h\" (the altitude) of this triangle, drawn to hypotenuse.\r\n" );
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document.write( "From the area consideration, we have this equation\r\n" );
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document.write( "     = .\r\n" );
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document.write( "It gives  h =  = 0.970143.\r\n" );
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document.write( "So, it is not 1 unit, as you see.\r\n" );
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document.write( "It means that the legs of the triangle should be    as long, as 1 unit and 4 units of the original triangle.\r\n" );
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document.write( "So, the area of the seeking triangle is   =  = .    ANSWER\r\n" );
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document.write( "ANSWER.  The area of the triangle under the question is  .\r\n" );
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