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Question
Three consecutive vertices of a parallelogram ABCD are A(S, 5), B(-7, -5) and C(-5, 5). Find the coordinates of the fourth vertex D.
Solution
we know that in a parallelogram diagonals bisect each other
∴ midpoint of AC = midpoint of BD
`"O" ((8 - 5)/2 , (5 + 5)/2) = "O"(("x" - 7)/2 , ("y" - 5)/2)`
`(8 - 5)/2 = ("x" - 7)/2 , (5 + 5)/2 = ("y" - 5)/2`
`3/2 = ("x" - 7)/2 , 10 = "y" - 5`
x = 10 , y = 15
Coordinates of fourth vertex D are (10 , 15)
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