document.write( "Question 1179379: Find the value(s) of y such that the triangle with the given vertices has an area of 8 square units. (Enter your answers as a comma-separated list.)
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Algebra.Com's Answer #808914 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "Find the value(s) of y such that the triangle with the given vertices has an area of 8 square units.
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document.write( "Let  A = (-4,5)\r\n" );
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document.write( "     B = (-3,3)\r\n" );
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document.write( "     C = (-3,y)\r\n" );
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document.write( "Notice that the side  BC  is vertical line  x= -3  of the length of  |y-3|     (absolute value).\r\n" );
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document.write( "Also notice that the distance of the point A from this line x= -3  is  -3 - (-4) = -3 + 4 = 1 unit.\r\n" );
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document.write( "    You may consider the side  BC  of the length  |y-3|  units as a base of the triangle  ABC,\r\n" );
document.write( "    and consider the distance of the point A from the line x= 3 as the length of the altitude\r\n" );
document.write( "    of this triangle drawn to the base BC.\r\n" );
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document.write( "So, your equation for the triangle area is\r\n" );
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document.write( "     = 8,\r\n" );
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document.write( "or\r\n" );
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document.write( "    |y - 3| = 16.\r\n" );
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document.write( "This equation has two solutions  y= 3+16 = 19  and  y= 3-16 = -13.\r\n" );
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document.write( "ANSWER.  There are two solutions for y:  y= -13  or  y= 19.\r\n" );
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