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Byju's Answer
Standard IX
Mathematics
Distance Formula
Show that □ L...
Question
Show that
□
LMNP is a square if L(
-
2,4) M(4,2), N(2,
-
4) and P (
-
4,
-
2) are the co-ordinate of the vertices.
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Solution
Given
:
L
≡
-
2
,
4
,
M
≡
4
,
2
,
N
≡
2
,
-
4
,
P
≡
-
4
,
-
2
Now
,
LM
=
4
-
-
2
2
+
2
-
4
2
=
6
2
+
-
2
2
=
36
+
4
=
40
=
2
10
units
MN
=
2
-
4
2
+
-
4
-
2
2
=
-
2
2
+
-
6
2
=
4
+
36
=
40
=
2
10
units
NP
=
-
4
-
2
2
+
-
2
-
-
4
2
=
-
6
2
+
2
2
=
36
+
4
=
40
=
2
10
units
LP
=
-
4
-
-
2
2
+
-
2
-
4
2
=
-
2
2
+
-
6
2
=
4
+
36
=
40
=
2
10
units
LN
=
2
-
-
2
2
+
-
4
-
4
2
=
4
2
+
-
8
2
=
16
+
64
=
80
=
4
5
units
MP
=
-
4
-
4
2
+
-
2
-
2
2
=
-
8
2
+
-
4
2
=
16
+
64
=
80
=
4
5
units
In
□
PQRS
,
side
LM
=
side
MN
=
side
NP
=
side
LP
and
diagonal
LN
=
diagonal
MP
.
∴
□
PQRS
is
a
square
.
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Q.
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□
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-
2,6), Q(3,1), R(
-
1,
-
3) and S(
-
6,2) are the co-ordinates of the vertices.
Q.
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