SOLUTION: Tell whether the points are the vertices of a parallelogram (that is not a rectangle), a rectangle, or neither. (-7, -1), (2, -10), (16, -3), (7, 8)

Algebra ->  Graphs -> SOLUTION: Tell whether the points are the vertices of a parallelogram (that is not a rectangle), a rectangle, or neither. (-7, -1), (2, -10), (16, -3), (7, 8)      Log On


   

Question 43450: Tell whether the points are the vertices of a parallelogram (that is not a rectangle), a rectangle, or neither.

(-7, -1), (2, -10), (16, -3), (7, 8)
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let the points be A (-7, -1), B (2, -10), C (16, -3) and D (7, 8).

Slope of AB = %28-1+-+%28-10%29%29%2F%28-7+-+2%29 = %28-1%2B10%29%2F%28-9%29 = -+9%2F9 = -1
Slope of BC = %28-10-%28-3%29%29%2F%282-16%29 = %28-10%2B3%29%2F%28-14%29 = +7%2F14 = 1%2F2
Slope of CD = %28-3+-+8%29%2F%2816+-+7%29 = -11%2F9
Slope of AB = %288+-+%28-1%29%29%2F%287+-%28-7%29%29 = %288%2B1%29%2F%287%2B7%29 = +9%2F14

For a quadrilateral to be a parallelogram, the opposite sides must be parallel and their slopes have to be equal.
So, here, slopes of AB and CD must be equal and also slopes of AC and BD must be equal.
Clearly, this is not the case.
Hence the given points does not form a parallelogram and so no question of rectangle.