document.write( "Question 390390: a triangle has an area of 6 square units. I t has vertices with coordinates(1,-3),(4,2) and a point on the x-axis. find all possible coordinates for this point \n" ); document.write( "

Algebra.Com's Answer #276879 by robertb(5830) $\"\"$ $\"About$

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The area of any triangle having vertices (a,b), (c,d), (e,f) is given by the absolute value of
\n" ); document.write( " $\"det%28%28matrix%283%2C3%2C+a%2Cb%2C1%2Cc%2Cd%2C1%2C+e%2Cf%2C+1%29%29%29%2F2\"$ . Hence we want absolute value of \r
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\n" ); document.write( "\n" ); document.write( " $\"det%28%28matrix%283%2C3%2C+1%2C-3%2C1%2C4%2C2%2C1%2C+x%2Cy%2C+1%29%29%29%2F2+\"$ = 6 or , after evaluating and simplifying the determinant, \r
\n" ); document.write( "\n" ); document.write( "|3y - 5x + 14| = 12. This is equivalent to 2 linear equations, namely \r
\n" ); document.write( "\n" ); document.write( "3y - 5x = -2, OR\r
\n" ); document.write( "\n" ); document.write( "3y - 5x = -26.\r
\n" ); document.write( "\n" ); document.write( "Any point with coordinates satisfying either equation would form with the other two points a triangle of area 6. \n" ); document.write( "

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