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Byju's Answer
Standard X
Mathematics
Length of Arc of a Sector
The centre of...
Question
The centre of a circle is
C
(
1
,
2
)
and one end of a diameter is
A
(
3
,
5
)
, find the coordinates of the other end.
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Solution
Let the other end of the diameter of the given circle be
B
(
α
,
β
)
whose one end is
A
(
3
,
5
)
Midpoint of
A
B
=
(
α
+
3
2
,
β
+
5
2
)
Since the centre
C
(
1
,
2
)
of the circle is the mid-point of
A
B
,
α
+
3
2
=
1
and
β
+
5
2
=
2
⇒
α
+
3
=
2
and
β
+
5
=
4
⇒
α
=
2
−
3
=
−
1
and
β
=
4
−
5
=
−
1
∴
The coordinates of the other end of the diameter are
(
−
1
,
−
1
)
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Similar questions
Q.
The centre of a circle is
C
(
3
,
5
)
and one end of a diameter is
A
(
4
,
3
)
, find the coordinates of the other end.
Q.
The coordinates of one end point of a diameter of a circle are (4, -1) and the coordinates of the centre of the circle are (1, -3). Find the coordinates of the other end of the diameter.
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