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ICSE Class X Math 2015 Solved Paper

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Three vertices of a parallelogram ABCD taken in order are A(3,6),B(5,10) and C(3, 2) find:
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Question : 7
Total: 52
the coordinates of the fourth vertex D.
Solution:  
Let the coordinate of D be (x,y). In a parallelogram, mid point of diagonal AC coincides with the mid-point of diagonal BD.

Mid point of AC=(‌
3+3
2
,‌
6+2
2
)=(3,4)
Mid point of BD=(‌
x+5
2
,‌
y+10
2
)
∵ Mid point of AC= Mid point of BD
(3,4)=(‌
x+5
2
,‌
y+10
2
)
Equating,
‌3=‌
x+5
2
‌ and ‌4=‌
y+10
2

‌x=1‌‌‌ and ‌y=−2
Coordinates of the fourth vertex D(1,−2)
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