document.write( "Question 1017250: http://prntscr.com/9xsn9a
\n" ); document.write( "The answers are parallelogram, rectangle, square, and rhombus.
\n" ); document.write( "The correct answer is rhombus, but I'm confused how?
\n" ); document.write( "I plugged the diagonals into the slope formula and my final result when I multiplied the products of the slopes was 0/0 each time.
\n" ); document.write( "Z (-4,2)
\n" ); document.write( "W(1,5)
\n" ); document.write( "X(5,2)
\n" ); document.write( "Y(1,-1)\r
\n" ); document.write( "\n" ); document.write( "I got 0/9 for 2-2 over 5--4 which results in 0/9.
\n" ); document.write( "I got -6/0 for -1-5 over 1-1 which results in -6/0 and then I multiplied 0/9 and -6/0 which gave me 0/0, but for the parallelogram to be a rhombus the product of the slopes has to be -1 and I got 0/0. So, I'm not sure why the correct answer is a rhombus. By the way, I got parallelogram for my answer. \n" ); document.write( "

Algebra.Com's Answer #633592 by MathTherapy(10556) $\"\"$ $\"About$

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\n" ); document.write( "The answers are parallelogram, rectangle, square, and rhombus.
\n" ); document.write( "The correct answer is rhombus, but I'm confused how?
\n" ); document.write( "I plugged the diagonals into the slope formula and my final result when I multiplied the products of the slopes was 0/0 each time.
\n" ); document.write( "Z (-4,2)
\n" ); document.write( "W(1,5)
\n" ); document.write( "X(5,2)
\n" ); document.write( "Y(1,-1)\r
\n" ); document.write( "\n" ); document.write( "I got 0/9 for 2-2 over 5--4 which results in 0/9.
\n" ); document.write( "I got -6/0 for -1-5 over 1-1 which results in -6/0 and then I multiplied 0/9 and -6/0 which gave me 0/0, but for the parallelogram to be a rhombus the product of the slopes has to be -1 and I got 0/0. So, I'm not sure why the correct answer is a rhombus. By the way, I got parallelogram for my answer.
\n" ); document.write( "

First, Z is not (- 4, 2), but (- 3, 2) instead. Maybe this is the reason why you’re not seeing a rhombus.\r
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document.write( "This is strategy I would use:
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document.write( "As seen, XZ and WY are its diagonals. Now, the length of diagonal XZ is 8 units, since the points' y coordinates (2) are the same, which
\n" );
document.write( "means that the diagonal, XZ is a horizontal line that's parallel to the x-axis. Therefore, this diagonal's length is the difference
\n" );
document.write( "between its x-coordinates, or 5 - - 3, or 8 units\r
\n" );
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document.write( "Likewise, the length of diagonal: WY is 6, since the points' x coordinates are the same, which means that the diagonal, WY is a vertical
\n" );
document.write( "line that's parallel to the y-axis. Therefore, this diagonal's length is the difference between its y-coordinates, or 5 - - 1, or 6 units\r
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document.write( "With the above information, a rectangle and square can be eliminated, since these quadrilaterals' diagonals are congruent. This leaves
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document.write( "2 choices: a parallelogram or a rhombus.\r
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document.write( "One major difference between the two is that the rhombus' sides are all congruent, while the parallelogram's are not. Taking two adjacent
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document.write( "sides: WX and XY, we find that the length of WX, using the distance formula, is: 5 units, while the length of XY, using the distance
\n" );
document.write( "formula is also 5 units. You could also test the other pair of adjacent sides: WZ and ZY, but this isn’t necessary. 
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document.write( "Thus, the quad WXYZ is proven to be a . \n" );
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