Sum

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.

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#### Solution

Let the coordinates of R and S be (x, y) and (a, b) respectively.

Mid-point of PR is O.

`therefore 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.

`therefore 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).

Concept: The Mid-point of a Line Segment (Mid-point Formula)

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