2. Show that the points |i rangle(-3,1),(-6,-7),(3,-9),(6,-1) taken in order form a parallelogram.
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Answer:
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=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
, we find
AB
2
=(5+7)
2
+(10+3)
2
=12
2
+13
2
=144+169=313
BC
2
=(15−5)
2
+(8−10)
2
=10
2
+(−2)
2
=100+4=104
CD
2
=(3−15)
2
+(−5,−8)
2
=(−12)
2
+(−13)
2
=144+169=313
DA
2
=(3+7)
2
+(−5+3)
2
=10
2
+(−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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