SOLUTION: Give the best name for a quadrilateral whose vertices have the given coordinates. B(-3, 0) F(-2, 7) J(5, 8) N(4, 1)

Question 419349: Give the best name for a quadrilateral whose vertices have the given coordinates.
B(-3, 0) F(-2, 7) J(5, 8) N(4, 1)
Answer by duckness73(47) (Show Source): You can put this solution on YOUR website!
The answer is "rhombus". Recall that the definition of a rhombus is a quadrilateral with all sides of equal length.
The length of any of these line segments = where a is the difference in the y-coordinates and b is the difference in the x-coordinates. Looking at segment FJ we find that the length = = = . The length of BF = = = . The length of BN = = = . The length of NJ = = = . Since all sides are equal, we have a rhombus.
What we don't know yet is whether the rhombus is a square. If the figure was a square, that would mean that adjacent sides would be perpendicular. Two lines are perpendicular when their slopes are negative reciprocals of each other. Let's examine any two adjacent sides, say FJ and NJ. The slope of FJ = ((8 - 7)/(5 - (-2)) = 1/7. The slope of NJ = (8 - 1)/(5 - 4) = 7/1 = 7. Although the slopes are reciprocals, they are NOT negative reciprocals, so the lines are not perpendicular. The figure is not a square, but it is still a rhombus.
Answer: rhombus

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