Answer :

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


Distance of AD


AD = √ ((15 – 3)2 + (9 – (–5))2)


AD = √ ((15 – 3)2 + (9 + 5)2)


AD = √ ((12)2 + (14)2)


AD = √ (144 + 196)


AD = √ 340


So, AB = CD = √65 and BC = AD = √340


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


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