the point ( 3,-4) is the centre of a circle. if AB is a diameter and B is (5, -6) find A.
Answers
Answer:
good afternoon all of uou
Answer:
Let us assume that C is the center and AB is a diameter of a circle.
Then C is the midpoint of AB.
One endpoint of AB is:
B
=
(
x
1
,
y
1
)
=
(
5
,
−
6
)
.
Let us assume the other endpoint to be:
A
=
(
x
2
,
y
2
)
.
The midpoint of AB is
C
=
(
3
,
−
4
)
.
Using the midpoint formula, we get:
C
=
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
(
3
,
−
4
)
=
(
5
+
x
2
2
,
−
6
+
y
2
2
)
3
=
5
+
x
2
2
;
−
4
=
−
6
+
y
2
2
[
Comparing the corresponding coordinates
]
6
=
5
+
x
2
;
−
8
=
−
6
+
y
2
[
Multiplied each equation on both sides by 2
]
x
2
=
1
;
y
2
=
−
2
Therefore, missing endpoint is:
A
=
(
x
2
,
y
2
)
=
(
1
,
−
2
)
Step-by-step explanation:
Let us assume that C is the center and AB is a diameter of a circle.
Then C is the midpoint of AB.
One endpoint of AB is:
B
=
(
x
1
,
y
1
)
=
(
5
,
−
6
)
.
Let us assume the other endpoint to be:
A
=
(
x
2
,
y
2
)
.
The midpoint of AB is
C
=
(
3
,
−
4
)
.
Using the midpoint formula, we get:
C
=
(
x
1
+
x
2
2
,
y
1
+
y
2
2
)
(
3
,
−
4
)
=
(
5
+
x
2
2
,
−
6
+
y
2
2
)
3
=
5
+
x
2
2
;
−
4
=
−
6
+
y
2
2
[
Comparing the corresponding coordinates
]
6
=
5
+
x
2
;
−
8
=
−
6
+
y
2
[
Multiplied each equation on both sides by 2
]
x
2
=
1
;
y
2
=
−
2
Therefore, missing endpoint is:
A
=
(
x
2
,
y
2
)
=
(
1
,
−
2
)