document.write( "Question 1022010: one vertex of a rhombus is at point (3,4). one diagonal of the rhombus lies along the line x-y-1=0 and two of the sides are parallel to the straight line 4x-3y+4=0.Find the remaining three vertices of the rhombus. \n" ); document.write( "

Algebra.Com's Answer #637679 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Here is what we are given.  The green line is the line x-y-1=0.\r\n" );
document.write( "The dotted red line is the line 4x-3y+4=0. The plotted point is\r\n" );
document.write( "(3,4)\r\n" );
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document.write( "First we find the equation of the left side of the rhombus.\r\n" );
document.write( "So we find the equation of a line parallel to the red dotted line\r\n" );
document.write( "that passes through the given point.\r\n" );
document.write( "By solving the equation of the red dotted line for y, we find its\r\n" );
document.write( "slope to be 4/3.  So we find the equation of the line through (4,3)\r\n" );
document.write( "with slope 4/3.  That turns out to be the line y = 4/3x.  That is\r\n" );
document.write( "the blue line below:\r\n" );
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document.write( "Next we find the lower left vertex of the rhombus by \r\n" );
document.write( "solving the system of the blue line and the green line\r\n" );
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document.write( "and find that vertex to be (-3,-4).\r\n" );
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document.write( "We now can find the other two vertices simply by counting \r\n" );
document.write( "blocks. Let's put it on graph paper:\r\n" );
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document.write( "By counting to go from vertex (-3,-4) to vertex (3,4),\r\n" );
document.write( "we must go 8 blocks up and 6 blocks right. Therefore to\r\n" );
document.write( "get to the other vertex we must go 8 blocks right and\r\n" );
document.write( "6 blocks up. That puts us at the point (5,2) which is\r\n" );
document.write( "the third vertex of the rhombus.  Then from (5,2) we\r\n" );
document.write( "count 6 blocks right and 8 blocks up, which puts us at\r\n" );
document.write( "the point (11,10), the fourth and final vertex of the\r\n" );
document.write( "rhombus.  So we plot those points, and draw the rhombus:\r\n" );
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document.write( "The reason it works to count blocks is because the \r\n" );
document.write( "three red right triangles drawn below with blue\r\n" );
document.write( "hypotenuses which are the sides of the rhombus, are \r\n" );
document.write( "all congruent and their hypotenuses are all equal \r\n" );
document.write( "in length making the four blue equal sides of the \r\n" );
document.write( "rhombus.  Note that we could also have found vertex \r\n" );
document.write( "(11,10) by counting blocks going from (3,4) to \r\n" );
document.write( "(11,10), counting 8 blocks up and 6 blocks right.  \r\n" );
document.write( "We traveled along the sides of those right triangles \r\n" );
document.write( "6 units one way and 8 units the other, which is why \r\n" );
document.write( "the red right triangles with blue hypotenuses\r\n" );
document.write( "are congruent.\r\n" );
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document.write( "So the vertices of the rhombus are\r\n" );
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document.write( "(3,4), given, (-3,-4), (5,2) and (11,10).\r\n" );
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document.write( "Edwin

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