# Show that A(1,0) , B(0,1), C(1,2) and D(2,1) are vertices of a parallelogram ABCD. Is ABCD a rectangle ?

2
by shivam2000

2015-03-13T13:09:56+05:30

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A(1,0)
b(0,1)
c(1,2)
d(2,1)

AB²=(X2-X)²+(Y2-Y)²
= (0-1)²+(1-0)²
=1+1
AB=√2
BC²=(1-0)²+(2-1)²=2
BC=√2
CD²=(2-1)²+(1-2)²=2
CD=√2

USE PYTHAGORIAN THEROM
AC²=2+2=4
AC=2

THEN WE CAN SAY THAT ΔADC IS A RIGHT-ANGLED TRIANGLE

AB²+BC²=AC²
SAME
ΔABC IS A RIGHT-ANGLED TRIANGLE

SO ABCD IS A SQUARE

PLZ PICK IT AS THE BEST...IF IT HELPZ..
i will add the pic..when i am able to edit it..
2015-03-13T15:02:33+05:30

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Distance between two points =

AB =

BC =

CD =

DA =

Since all sides are equal, its a parallelogram

It could be a rhombus or a square