document.write( "Question 864720: SHOW in two ways that (0,-5) (3,-4) (8,0) and (5,-1) are the vertices of a rhombus. PLEASSSE HELP! \n" ); document.write( "
Algebra.Com's Answer #521232 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
From the definition of a Rhombus, we know that all four sides are of equal length ,the opposite sides are parallel and the diagonals are of equal length.
\n" ); document.write( "we will use the following math concepts
\n" ); document.write( "distance (d) between two points = square root ( (x2-x1)^2 + (y2-y1)^2 )
\n" ); document.write( "two lines are parallel if they have the same slope (m)
\n" ); document.write( "m is defined as (y2 - y1) / (x2 - x1)
\n" ); document.write( "we are given the vertices (0,-5) (3,-4) (8,0) and (5,-1) and label them A,B,C,D
\n" ); document.write( "d(AB) = square root ( 3^2 + 1^2 ) = square root (10)
\n" ); document.write( "d(CD) = square root ( -3^2 + -1^2) = square root (10)
\n" ); document.write( "d(BC) = square root ( 5^2 + 4^2) = square root (41)
\n" ); document.write( "d(AD) = square root ( 5^2 + 4^2) = square root (41)
\n" ); document.write( "d(AC) = square root ( 8^2 + 5^2) = square root (89)
\n" ); document.write( "d(BD) = square root ( 2^2 + 3^2) = square root (13)
\n" ); document.write( "m(AB) = 1/3
\n" ); document.write( "m(CD) = -1/-3 = 1/3
\n" ); document.write( "m(BC) = 4/5
\n" ); document.write( "m(AD) = 4/5
\n" ); document.write( "m(AC) = 5/8
\n" ); document.write( "m(BD) = 3/2
\n" ); document.write( "AB and CD are parallel and equal length
\n" ); document.write( "BC and AD are parallel and equal length
\n" ); document.write( "AC and BD are not parallel or perpendicular and are of unequal length
\n" ); document.write( "this is NOT a rhombus\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );