Question 1159255: The vertices of a quadrilateral are (4.6), (7,2), (-1, -5), and (-4,3). Which is the best classification for the quadrilateral.
Multiple Choice:
A. parallelogram
B. rhombus
C. rectangle.
D square
Thank you :)
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
A very rough sketch of the four given points shows that it is not any of those shapes.
Check the given coordinates and re-post the problem with the correct ones.
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I could see that the point was supposed to be (7,-2) instead of (7,2) from the rough sketch....
Here is a sketch pirated from the other tutor's response, with the corrected coordinates of that point.
Now it looks very much like a square; and some simple calculations confirm that it is.
From A to B and from D to C are both right 3 and down 8, so those segments have the same slope (-8/3) and the same length.
And from D to A and from C to B are both right 8 and up 3, so those segments also have the same slope (3/8) and the same length.
So all four sides of the quadrilateral have the same length, and the slopes of the two pairs of parallel sided are negative reciprocals; and that makes the quadrilateral a square.
Answer by MathLover1(20850)  (Show Source):
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