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Byju's Answer
Standard IX
Mathematics
Equations with Two Variables
Is the line (...
Question
Is the line (-2,3)and (4,1) perpendicular to the line 3x = y+1 ? Does the line3x= y+1 bisect the join of(-2,3)and (4,1) ?
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Solution
Slope
of
the
line
l
1
joining
(
x
1
,
y
1
)
=
(
-
2
,
3
)
and
(
x
2
,
y
2
)
=
(
4
,
1
)
is
given
by
m
1
=
y
2
-
y
1
x
2
-
x
1
=
1
-
3
4
+
2
=
-
2
6
=
-
1
3
Now
the
equation
of
the
second
line
l
2
is
3
x
=
y
+
1
⇒
y
=
3
x
-
1
By
comparing
with
it
with
y
=
m
2
x
+
c
we
get
m
2
=
3
Now
since
m
1
m
2
=
-
1
3
×
3
=
-
1
Hence
product
of
slope
of
lines
l
1
and
l
2
is
-
1
,
so
both
lines
are
perpendicular
.
Now
for
the
another
part
of
question
Mid
point
of
line
l
1
joining
(
x
1
,
y
1
)
=
(
-
2
,
3
)
and
(
x
2
,
y
2
)
=
(
4
,
1
)
is
given
by
P
=
x
2
+
x
1
2
,
y
2
+
y
1
2
=
-
2
+
4
2
,
1
+
3
2
=
(
1
,
2
)
Now
second
line
l
2
:
3
x
=
y
+
1
is
satisfied
by
the
point
P
(
1
,
2
)
,
because
3
×
1
=
2
+
1
,
So
the
mid
point
of
line
l
1
lies
on
the
line
l
2
:
3
x
=
y
+
1
.
Hence
line
3
x
=
y
+
1
bisect
The
the
line
l
1
joining
(
x
1
,
y
1
)
=
(
-
2
,
3
)
and
(
x
2
,
y
2
)
=
(
4
,
1
)
.
Suggest Corrections
0
Similar questions
Q.
Is the line through
(
−
2
,
3
)
and
(
4
,
1
)
perpendicular to the line
3
x
=
y
+
1
? Does the line
3
x
=
y
+
1
bisect the line joining of
(
−
2
,
3
)
and
(
4
,
1
)
?
Q.
If two points
P
=
(
0
,
–
1
)
and
Q
=
(
4
,
1
)
are on a straight line, find equation of the Straight line.
Q.
Through the point
P
(
4
,
1
)
a line is drawn to meet the line
3
x
−
y
=
0
at
Q
where
P
Q
=
11
/
(
2
√
2
)
. Determine the equation of the line.
Q.
Solve the following simultaneous equations:
1
3
x
+
y
+
1
3
x
−
y
=
3
4
,
1
2
(
3
x
−
y
)
−
1
2
(
3
x
−
y
)
=
−
1
8
Q.
Equation of the line passing through (1, 2) and parallel to the line
y
=
3
x
–
1
is
.
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