Question

prove that the points (-7,-3) (-1,2) (8,5) and (5.-4)
taken on older are
the corners of a paralognan​

Answer 1

$Let A, B, C and D represent the points (-7, -3), (5, 10), (15, 8) and (3, -5) respectively. </p><p>Using the distance formula d=(x2−x1)2+(y2−y1)2, we find</p><p>AB2=(5+7)2+(10+3)2=122+132=144+169=313</p><p>BC2=(15−5)2+(8−10)2=102+(−2)2=100+4=104</p><p>CD2=(3−15)2+(−5,−8)2=(−12)2+(−13)2=144+169=313</p><p>DA2=(3+7)2+(−5+3)2=102+(−2)2=100+4=104</p><p>So, AB=CD=313 and BC=DA=104</p><p></p><p>$

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