Q. 6 B

# Show that the following points taken in order form the vertices of a parallelogram.(9, 5), (6, 0), (−2, −3) and (1, 2)

Formula used: (9,5), (6, 0), (–2, –3) and (1, 2)

Let A, B, C and D represent the points (9, 5), (6, 0), (–2, –3) and (1, 2)

Distance of AB

AB = √ ((6 – 9))2 + (0 – 5)2)

AB = √ ((–3)2 + (5)2)

AB = √ (9 + 25)

AB = √ 34

Distance of BC

BC= √ ((–2 – 6)2 + (–3 – 0)2)

BC = √ ((–8)2 + (–3)2)

BC = √ (64 + 9)

BC = √73

Distance of CD

CD = √ ((1 – (–2))2 + (2 – (–3))2)

CD = √ ((1 + 2)2 + (2 + 3))2)

CD = √ ((3)2 + (5)2)

CD = √ (9 + 25)

CD = √36

AD = √ ((1 – 9))2 + (2 – 5)2)

AD = √ ((–8)2 + (–3)2)

AD = √ (64 + 9)

So, AB = CD = √36 and BC = AD = √73

i.e., The opposite sides are equal. Hence ABCD is a parallelogram.

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