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Hannahrose911
21.01.2020 •
Mathematics
Which statement best describes a parallelogram with coordinates a (-1, 0), b (-4, 5), c (1, 8) and d (4, 3)? a. the diagonals are congruent which means the quadrilateral is a rectangle. b. the diagonals are perpendicular which means the quadrilateral is a rhombus. c. the diagonals are both congruent and perpendicular which means the quadrilateral is a square. d. the diagonals are neither congruent nor perpendicular, which means the quadrilateral is a parallelogram only.
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Ответ:
D.
Step-by-step explanation:The representation of this problem is shown below. To find the answer, we need to use the distance formula:
![The \ \mathbf{distance} \ d \ between \ the \ \mathbf{points} \ (x_{1},y_{1}) \ and \ (x_{2},y_{2}) \ in \ the \ plane \ is:\\ \\ d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](/tpl/images/0464/4728/0b59d.png)
The first diagonal is formed by the points A and CThe second diagonal is formed by the points B and DSo, for the first diagonal:
For the second diagonal:
So the diagonals aren't congruent. Are they perpendicular?
These two vectors will be perpendicular (hence the diagonals will be perpendicular) if and only if the dot product equals zero, so:
Thus, the diagonals aren't perpendicular. In conclusion:
D. The diagonals are neither congruent nor perpendicular, which means the quadrilateral is a parallelogram only.Ответ:
x² + 6x = 31 - 9
x² + 6x + 9 = 31
(x+3)² = 31