# The vertices of a quadrilateral are A(-4, -2), B(2, 6), C(8, 5) and D(9, -7). Using slopes, show that the midpoints of the sides of the quad. ABCD from a parallelogram. The vertices of the given quadrilateral are A(-4,-2) B(2, 6), C(8, 5) and D(9, -7)

The mid point of a line A(x1,y1) and B(x2,y2) is found out by Now midpoint of AB = The midpoint of BC = The midpoint of CD = Midpoint of DA = So now we have four points

P(-1,2),Q(5,5.5),R(8.5,-1),S(2.5,-4.5) Slope of PQ = Slope of QR = Slope of RS = Slope of SP = Now we can observe that slope of PQ = RS and slope of QR = SP

Which shows that line PQ is parallel to RS and line QR is parallel to SP

Also, the product of two adjacent lines is not equal to -1

Therefore PQRS is a parallelogram.

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