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Question
If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are ______.
Options
(–2, – 1)
(–2, –3)
(2, –1)
(1, 2)
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Solution
If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are (2, –1).
Explanation:
Since PQRS is a parallelogram
It's Diagonals bisect each other
Therefore, Midpoint of PR = Midpoint of QS
`((3 + (-3))/2, (4 + (-2))/2) = ((-2 + x)/2, (3 + y)/2)`
`(0, 2/2) = ((-2 + x)/2, (3 + y)/2)`
Comparing x-coordinate
0 = `(-2 + x)/2`
0 = –2 + x
x = 2
Comparing y-coordinate
`2/2 = (3 + y)/2`
2 = 3 + y
y = –1
∴ Coordinates of point S is (2, –1)
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