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.!