Question

Prove that the points (-7, -3), (5, 10), (15, 8) and (3,-5) taken in order are the corners of a parallelogram.​

Answer 1

Step-by-step explanation:

Let A, B, C and D represent the points (-7, -3), (5, 10), (15, 8) and (3, -5) respectively.

Using the distance formula d=(x2−x1)2+(y2−y1)2, we find

AB2=(5+7)2+(10+3)2=122+132=144+169=313

BC2=(15−5)2+(8−10)2=102+(−2)2=100+4=104

CD2=(3−15)2+(−5,−8)2=(−12)2+(−13)2=144+169=313

DA2=(3+7)2+(−5+3)2=102+(−2)2=100+4=104

So, AB=CD=313 and BC=DA=104

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

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