Question

Show that each quadrilateral with the given vertices is a parallelogram.

N(5,1), P(2,7), Q(6,9), R(9,3)

Answer 1

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Step-by-step explanation:

The quadrilateral is a parallelogram if the midpoints of its diagonals are the same point. That is, if ...

(N +Q)/2 = (P +R)/2

Multiplying by 2, we can simplify the test to ...

N +Q = P +R

(5, 1) +(6, 9) = (2, 7) +(9, 3)

(5+6, 1+9) = (2+9, 7+3)

(11, 10) = (11, 10) . . . . . . . true ∴ NPQR is a parallelogram