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Question
P(4, 2) and Q(–1, 5) are the vertices of parallelogram PQRS and (–3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.
Solution
Let the coordinates of R and S be (x, y) and (a, b) respectively.
Mid-point of PR is O.
∴ `O(-3, 2) = O((4 + x)/2, (2 + y)/2)`
`-3 = (4 + x)/2, 2 = (2 + y)/2`
−6 = 4 + x, 4 = 2 + y
x = −10, y = 2
Hence, R = (−10, 2)
Similarly, the mid-point of SQ is O.
∴ `O(-3, 2) = O((a - 1)/2, (b + 5)/2)`
`-3 = (a - 1)/2, 2 = (b + 5)/2`
−6 = a – 1, 4 = b + 5
a = −5, b = –1
Hence, S = (−5, −1)
Thus, the coordinates of the point R and S are (−10, 2) and (−5, −1).
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