If ABCD is a parallelogram with A (5,4), B (-1,-2), C (8,-2). How do you find the coordinates of D?

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Answer 1 · 2016-09-22T18:12:55

Thus, the fourth vertex of the prlgm. can be

$D(-4,4), D(14,4), or, D(2,-8)$ .

Let the fourth vertex of the prlgm. be $D(x,y).$

Now, there are $3$ possibilities :-

$"Case (1) : "AB and CD" are Diagonals"$ :-

We know that the diagonals of a prlgm. bisect each other.

$:. "Mid-pt dig".AB="Mid-pt. of dig". CD$

$:. ((5-1)/2,(4-2)/2)=((x+8)/2,(y-2)/2)$

$:. x+8=4, y-2=2$

$:. x=-4, y=4$

#:. D(x,y)=D(-4,4) in this case.

$"Case (2) : "AC and BD" are Diagonals"$ :-

Proceeding as above, we have, In this case, $D(x,y)=D(14,4)$ .

$"Case (3) : "AD and BC" are Diagonals"$ :-

In this case, $D(x,y)=D(2,-8)$ .

Thus, the fourth vertex of the prlgm. can be

$D(-4,4), D(14,4), or, D(2,-8)$ .

Enjoy Maths.!