Show that the points (7,3) (3,0) (0,-4) (4,-1)are vertices of rhombus\

1.	Show that the points (7,3) (3,0) (0,-4) (4,-1)are vertices of rhombus\xa0\xa0
Answer» Let A(7,3) , B(3,0) , C(0,-4) and D(4,-1) represent the points.To prove that these points are vertices of a rhombus we have to show that all sides are equal. We may calculate it using distance formula.AB=\xa0(3-7)2+(0-3)2=\xa016+9=25=\xa05\xa0unitsBC=(0-3)2+(-4-0)2=9+16\xa0=25=5\xa0unitsCD=(4-0)2+(-1+4)2=16+9\xa0=25\xa0=\xa05unitsDA=(7-4)2+(3+1)2=9+16=25=5\xa0unitsThe diagonals are not equal.\xa0AC=\xa0(7-0)2+(3+4)2=49+49=98=72unitsBD=(4-3)2+(-1-0)2\xa0=\xa01+1\xa0=2unitsThis shows that these points are vertices of rhombus.

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