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.

Answer 1

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).