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shivam2000
@shivam2000
May 2021
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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 ?
Answers & Comments
Revolution
Verified answer
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
AD²=(2-1)²+(1-0)²=2
AD=√2
USE PYTHAGORIAN THEROM
AD²+DC²=AC²
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
1 votes
Thanks 2
Revolution
PLZ PICK IT AS THE BEST...IF IT HELPZ..
Revolution
i will add the pic..when i am able to edit it..
Mathexpert
Verified answer
Distance between two points =
AB =
BC =
CD =
DA =
Since all sides are equal, its a parallelogram
It could be a rhombus or a square
3 votes
Thanks 2
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Answers & Comments
Verified answer
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
AD²=(2-1)²+(1-0)²=2
AD=√2
USE PYTHAGORIAN THEROM
AD²+DC²=AC²
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
Verified answer
Distance between two points =AB =
BC =
CD =
DA =
Since all sides are equal, its a parallelogram
It could be a rhombus or a square