Sum

A (-1, 0), B (1, 3) and D (3, 5) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C.

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#### Solution

Let the co-ordinates of vertex C be (x, y).

ABCD is a parallelogram.

∴ Mid-point of AC = Mid-point of BD

`((-1+x)/2,(0+y)/2)=((1+3)/2,(3+5)/2)`

`((-1+x)/2,y/2)=(2,4)`

`(-1+x)/2=2 and y/2=4`

`x=5 and y/2=4`

`x=5 and y=8`

Thus, the co-ordinates of vertex C is (5, 8).

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

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