The endpoints of one diagonal of rhombus are (0,-8) and (8,-4). If the coordinates of the third vertex are (1,0). what are the coordinates of the forth vertex?

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Answer 1 · 2017-06-02T09:00:32

The coordinates are #=(7,-12)#

Let #A=(0,-8)#

#C=(8,-4)#

The midpoint of #AC# is

#E=((0+8)/2, (-8-4)/2)=(4,-6)#

Let #B=(1,0)# and #D=(x,y)#

The mid point of #BD# is

#E'=((x+1)/2,(y/2))#

#E and E'# is the same point

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

#=>#

#(x+1)/2=4#

#x+1=8#

#x=7#

#y=-12#

The point #D=(7,-12)#

Answer 2 · 2017-06-02T09:02:03

# (7,-12),# is the reqd. fourth vertex.

We know that a Rhombus is a Parallelogram, and, the

Diagonals of a parallelogram bisect each other.

This means that both the diagonals must have the same mid-point.

Hence, the midpt. of the diagonal through vertices

#(0,-8) and (8,-4)# is the same as that through the fourth vertex, say,

#(x,y) and (1,0).#

#:. ((0+8)/2,(-8-4)/2)=((x+1)/2,(y+0)/2).#

# :. 8=x+1, -12=y.#

# rArr (x,y)=(7,-12),# is the reqd. fourth vertex.

Enjoy Maths.!