Find equation of the perpendicular bisector of segment joining the points (2,−5) and (0,7)?
- Ax - 6y = 5
- Bx + 6y = -5
- Cx - 6y = -5
- Dx + 6y = 5
Solution & Step-by-step Explanation
Let the given points be A(2,−5) and B(0,7).
Find the midpoint of AB (since the perpendicular bisector passes through the midpoint):
Midpoint M=(
2
2+0
,
2
−5+7
)=(1,1)
Find the slope of AB (m
1
):
m
1
=
0−2
7−(−5)
=
−2
12
=−6
Find the slope of the perpendicular bisector (m
2
):
Since the lines are perpendicular, m
1
×m
2
=−1:
−6×m
2
=−1⟹m
2
=
6
1
Find the equation of the line passing through M(1,1) with slope m
2
=
6
1
:
y−y
1
=m
2
(x−x
1
)
y−1=
6
1
(x−1)
6(y−1)=x−1
6y−6=x−1
x−6y=−5
Find the midpoint of AB (since the perpendicular bisector passes through the midpoint):
Midpoint M=(
2
2+0
,
2
−5+7
)=(1,1)
Find the slope of AB (m
1
):
m
1
=
0−2
7−(−5)
=
−2
12
=−6
Find the slope of the perpendicular bisector (m
2
):
Since the lines are perpendicular, m
1
×m
2
=−1:
−6×m
2
=−1⟹m
2
=
6
1
Find the equation of the line passing through M(1,1) with slope m
2
=
6
1
:
y−y
1
=m
2
(x−x
1
)
y−1=
6
1
(x−1)
6(y−1)=x−1
6y−6=x−1
x−6y=−5