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Question
The three vertices of a parallelogram taken in order are (0, 1), (−1, −2), and (2, 1). The coordinates of fourth vertex are ______.
Options
(2, 3)
(3, 4)
(4, 3)
(3, 2)
MCQ
Fill in the Blanks
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Solution
The three vertices of a parallelogram taken in order are (0, 1), (−1, −2), and (2, 1). The coordinates of fourth vertex are (3, 4).
Explanation:
In a parallelogram, the diagonals bisect each other,
So the midpoint of AC:
= `((0 + 2)/2, (1 + 1)/2)`
= (1, 1)
Set this equal to the midpoint of BD:
= `((-1+x)/2, (-2+y)/2)`
(Multiplying both sides by 2)
= (−1 + x = 2), (−2 + y = 2)
∴ x = 3, y = 4
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