(ii) Show that A(3,5), B(1, 1), C(5, 3) and D(7,7)
are the vertices of a rhombus, is it a square? Find
its area.
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1
Answer:
Consider the problem
Given points are
A(7,5),B(2,3),C(6,−7)
Let the given lines of triangle be AB,BC,AC
Let , By distance formula
Distance of AB
AB=
(3−5)
2
+(2−7)
2
=
(−2)
2
+(−5)
2
=
4+25
=
29
Similarly,
BC=
(−7−3)
2
+(6−2)
2
=
100+16
=
116
AC=
(−7−5)
2
+(6−7)
2
=
145
Now, Pythagoras theorem
AC
2
=BC
2
+AB
2
(
145
)
2
=(
116
)
2
+(
29
)
2
145=116+29
145=145
L.H.S.=R.H.S
Hence, prove that they are at right angles.
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