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Byju's Answer
Standard XII
Mathematics
Distance Formula
ABCD is a squ...
Question
A
B
C
D
is a square. Points
E
(
4
,
3
)
and
F
(
2
,
5
)
lie on
A
B
and
C
D
, respectively, such that
E
F
divides the square in two equal parts. If the coordinates of
A
are
(
7
,
3
)
, the other coordinates of the vertices can be
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Solution
E
i
s
m
i
d
p
o
i
n
t
o
f
A
B
∴
c
o
o
r
d
i
n
a
t
e
o
f
B
(
x
,
y
)
⇒
x
+
7
2
=
4
⇒
x
=
1
,
3
+
y
2
=
3
,
y
+
3
=
6
,
y
=
3
and mid point of EF are point of interaction of diagonals.
(
4
+
2
2
)
=
3
,
(
3
+
5
2
)
=
4
∴
0
(
3
,
4
)
Hence coordinate of D,
⇒
x
1
+
1
2
=
3
,
x
1
+
1
=
−
6
,
x
1
=
5
y
1
+
3
2
=
4
,
y
1
+
3
=
8
,
y
=
5
and coordinate of C,
(
x
2
,
y
2
)
⇒
x
2
+
7
2
=
3
,
x
2
=
1
⇒
y
2
+
3
2
=
4
,
y
2
=
5
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Similar questions
Q.
Assertion :
A
B
C
D
is a square with vertices
(
0
,
0
)
,
(
1
,
0
)
,
(
1
,
1
)
and
(
0
,
1
)
.
P
,
Q
,
R
and
S
are the points which divide
A
B
,
B
C
,
C
D
,
D
A
respectively in the ratio
2
:
1
. If the origin is shifted to the centre of the square
A
B
C
D
without rotation of axes, area of the square
P
Q
R
S
in the new system of coordinates is
5
9
square units. Reason: If the origin is shifted to the point
P
(
α
,
β
)
without rotation of axes then the distance between any two given points remains unchanged in the new system of coordinates
Q.
A
(
3
,
4
)
and
C
(
1
,
−
1
)
are the two opposite angular points of a square ABCD. Find the coordinates of the other two vertices.
Q.
Let
A
B
C
D
is a square with sides of unit length .Points E and F are taken on sides
A
B
and
A
D
respectively so that
A
E
=
A
F
.Let P be a point inside the
□
A
B
C
D
.
Let a line passing through point
A
divides the square
□
A
B
C
D
into two parts so that area of one portion is double the other, then the length of portion of line inside the square is
Q.
Let
A
B
C
D
be a square of side 2a. Find the coordinates of the vertices of this square when (i) A coincides with the origin and AB and AD are along OX and OY respectively. (ii) The center of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.
Q.
Let
A
B
C
D
be a square such that vertices
A
,
B
,
C
,
D
lie on circles
x
2
+
y
2
−
2
x
−
2
y
=
0
,
x
2
+
y
2
−
2
x
−
2
y
+
1
=
0
,
x
2
+
y
2
+
2
x
+
2
y
+
1
=
0
and
x
2
+
y
2
−
2
x
+
2
y
+
1
=
0
respectively with center of square being origin and sides are parallel to coordinate axes. The length of side of such square can be
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