If the equation (a1 - a2)x + (61 – 62)y= C represents the
perpendicular bisector of the line segment joining
(aj, bi), (a2, b2), then 2 cis
Answers
Correct Question:-
If the equation represents the perpendicular bisector of the line segment joining
and
then find the value of
Solution:-
The midpoint of the line segment joining and
is
This point belongs to the perpendicular bisector of the line segment, i.e.,
Then,
Correct Question:-
If the equation (a_1-a_2)x+(b_1-b_2)y=c(a
1
−a
2
)x+(b
1
−b
2
)y=c represents the perpendicular bisector of the line segment joining (a_1,\ b_1)(a
1
, b
1
) and (a_2,\ b_2),(a
2
, b
2
), then find the value of 2c.2c.
Solution:-
The midpoint of the line segment joining (a_1,\ b_1)(a
1
, b
1
) and (a_2,\ b_2)(a
2
, b
2
) is \left(\dfrac{a_1+a_2}{2},\ \dfrac{b_1+b_2}{2}\right).(
2
a
1
+a
2
,
2
b
1
+b
2
).
This point belongs to the perpendicular bisector of the line segment, i.e., (a_1-a_2)x+(b_1-b_2)y=c.(a
1
−a
2
)x+(b
1
−b
2
)y=c.
Then,
\longrightarrow(a_1-a_2)\cdot\dfrac{a_1+a_2}{2}+(b_1-b_2)\cdot\dfrac{b_1+b_2}{2}=c⟶(a
1
−a
2
)⋅
2
a
1
+a
2
+(b
1
−b
2
)⋅
2
b
1
+b
2
=c
\longrightarrow(a_1-a_2)(a_1+a_2)+(b_1-b_2)(b_1+b_2)=2c⟶(a
1
−a
2
)(a
1
+a
2
)+(b
1
−b
2
)(b
1
+b
2
)=2c
\longrightarrow\underline{\underline{(a_1)^2-(a_2)^2+(b_1)^2-(b_2)^2=2c}}⟶
(a
1
)
2
−(a
2
)
2
+(b
1
)
2
−(b
2
)
2
=2c