Question

(-2, 4), (4, 8), (10, 7) and (11, -5) are the
vertices of a quadrilateral. Show that the
quadrilateral, obtained on joining the mid-points
of its sides, is a parallelogram.​

Answer 1

Answer:

Let A(-2,4), B(4,8), C(10,7), D(11,-5) be the vertices of a quadrilateral.

Let E, F, G, H be the mid points of the sides AB, BC, DC and AD respectively.

Then,

Coordinates of E are : (1,6)

Coordinates of F are : (7,215)

Coordinated of G are : (221,1)

Coordinates of H are : (29,2−1)

Now slope of EF = 41

Slope of GH = 41

Slope of EH = −713

Slope of FG = −713

Hence, opposite sides are parallel to each other.

Also, EF=GH and EH=FG

So, EFGH is a parallelogram.

Step-by-step explanation:

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