Show that ABCD is a square where
A, B, C, D are the points (0,4,1) (2,3,-1(4,5,0) and (2, 6, 2) respectively.
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Answer:
Answer
Given A(0,4,1) B(2,3,−1) C(4,5,0) D(2,6,2)
AB=
(0−2)
2
+(4−3)
2
+(1+1)
2
=3
BC=
(2−4)
2
+(3−5)
2
+(−1−0)
2
=3
CD=
(4−2)
2
+(5−6)
2
+(0−2)
2
=3
DA=
(2−0)
2
+(6−4)
2
+(2−1)
2
=3
∴AB=BC=CD=DA
AC=
(0−4)
2
+(4−5)
2
+(1−0)
2
=
18
BD=
(2−2)
2
+(3−6)
2
+(−1−2)
2
=
18
∴AC=BC.
∴AB
2
+BC
2
=AC
2
9+9=18.
∠ABC=90
o
∴A,B,C,D are vertices of square.
Step-by-step explanation:
I hope it help you
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