The three vertices of a parallelogram abcd are a(3,-4),b(-1,-3)and c(-6,2).find the coordinates of vertex d and findthe area of abcd
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The fourth coordinate can be found by first finding the bisecting point of diagonal
In parrallelogram ABCD
Let bisecting point of diagonal be O
since we know that in parrallelogram diagonal bisect each other
Therefore AO = CO and BO = DO
let co-ordinates of O be (x,y)
now by section formula you can find co-ordinates of O if m:n =1:1
i.e x=9/2 and y = -2
since you know the coordinates of O
now you can easily find coordinate of D by same section formula.
Area of parrallelogram = 2(area of 1 triangle formed by diagonal by cutting parrallelogram into two halves)
In parrallelogram ABCD
Let bisecting point of diagonal be O
since we know that in parrallelogram diagonal bisect each other
Therefore AO = CO and BO = DO
let co-ordinates of O be (x,y)
now by section formula you can find co-ordinates of O if m:n =1:1
i.e x=9/2 and y = -2
since you know the coordinates of O
now you can easily find coordinate of D by same section formula.
Area of parrallelogram = 2(area of 1 triangle formed by diagonal by cutting parrallelogram into two halves)
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