Quadrilateral PQRS has vertices #P(-9, -1), Q(-2, 4), R(4, 3), #and #S(9,-4)#. How do you prove that PQRS is a trapezoid?

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Answer 1 · 2017-03-13T09:18:49

As #QR#||#PS#, #PQRS# is a trapezoid

The slope of a line joining two points #(x_1,y_1)# and #(x_2,y_2)# is #(y_2-y_1)/(x_2-x_1)#.

Further the slopes of two parallel lines is equal.

Here slope of line joining #Q(-2,4)# and #R(4,3)# is

#(3-4)/(4-(-2))=(-1)/6=-1/6# and

slope of line joining #P(-9,-1)# and #S(9,-4)# is

#(-4-(-1))/(9-(-9))=(-4+1)/18=-3/18=-1/6#

As the slopes are equal, #QR#||#PS#

and #PQRS# is a trapezoid.