Q. 6 E5.0( 1 Vote )

# Show that the fol

Formula used: (3, –5), (–5, –4), (7, 10) and (15, 9)

Let A, B, C and D represent the points (3, –5), (–5, –4), (7, 10) and (15, 9)

Distance of AB

AB = √ ((–5 – 3)2 + ((–4 – (–5))2)

AB = √ ((–5 – 3))2 + (–4 + 5)2)

AB = √ ((–8)2 + (1)2)

AB = √ (64 + 1)

AB = √ 65

Distance of BC

BC= √ ((7 – (–5))2 + (10 – (–4))2)

BC= √ ((7 + 5)2 + (10 + 4)2)

BC = √ ((12)2 + (14)2)

BC = √ (144 + 196)

BC = √ 340

Distance of CD

CD = √ ((15 – 7)2 + (9 – 10)2)

CD = √ ((8)2 + (–1)2)

CD = √ (64 + 1)

CD = √65

AD = √ ((15 – 3)2 + (9 – (–5))2)

AD = √ ((15 – 3)2 + (9 + 5)2)

AD = √ ((12)2 + (14)2)

AD = √ (144 + 196)

So, AB = CD = √65 and BC = AD = √340

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

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