document.write( "Question 773946: Find the area of the triangle enclosed by the x-axis, the y-axis and the line y = 2x-6.\r
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Algebra.Com's Answer #471959 by ramkikk66(644) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The line, x axis and y axis form a right triangle, since x axis and y axis\r\n" );
document.write( "are perpendicular to each other. To find the area of the triangle, you need to\r\n" );
document.write( "know \r\n" );
document.write( "1) the value of the x intercept (the point where the line intersects the x axis):\r\n" );
document.write( "This is the length of one side of the triangle.\r\n" );
document.write( "2) the value of the y intercept (the point where the line intersects the y axis):\r\n" );
document.write( "This is the length of the perpendicular side of the triangle.\r\n" );
document.write( "3) To find the x intercept, substitute y as 0 in the equation. (Why? Because the\r\n" );
document.write( "x axis is represented by the equation y = 0, and the x intercept is where the line\r\n" );
document.write( "intersects the x axis)\r\n" );
document.write( "Putting y = 0, we get 2x - 6 = 0, or x = 3. So the x intercept = (3,0) and the \r\n" );
document.write( "length of the side of the triangle is 3.\r\n" );
document.write( "4) To find the y intercept, substitute x as 0 in the equation. (Why? Because the\r\n" );
document.write( "y axis is represented by the equation x = 0, and the y intercept is where the \r\n" );
document.write( "line intersects the y axis)\r\n" );
document.write( "Putting x = 0, we get y = 2x - 6 = -6. So the y intercept = (0,-6) and the \r\n" );
document.write( "length of the side of the triangle is 6.\r\n" );
document.write( "5) Since we know the length of the 2 perpendicular sides of the right triangle,\r\n" );
document.write( "the area is simply \r\n" );
document.write( "The graph of the line is given below for your reference. You can clearly see\r\n" );
document.write( "the 3 vertices of the triangle are (0,0), (3,0) and (0,-6) and the lengths of\r\n" );
document.write( "the 2 perpendicular sides are 3 units and 6 units as explained above.\r\n" );
document.write( "Hope you got it :)\r\n" );
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