4
You visited us
4
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Points of Trisection
Find the coor...
Question
Find the coordinates of points which trisect the line segment joining
(
1
,
−
2
)
a
n
d
(
−
3
,
4
)
.
Open in App
Solution
Using the section formula, if a point
(
x
,
y
)
divides the line joining the points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
in the ratio
m
:
n
, then
(
x
,
y
)
=
(
m
x
2
+
n
x
1
m
+
n
,
m
y
2
+
n
y
1
m
+
n
)
Let A
(
1
,
−
2
)
and
B
(
−
3
,
4
)
be the given points.
Let the points of trisection be
P
(
a
,
b
)
and
Q
(
c
,
d
)
.
Then,
A
P
=
P
Q
=
Q
B
=
λ
(
s
a
y
)
.
∴
P
B
=
P
Q
+
Q
B
=
2
λ
A
Q
=
A
P
+
P
Q
=
2
λ
⇒
A
P
:
P
B
=
λ
:
2
λ
=
1
:
2
a
n
d
A
Q
:
Q
B
=
2
λ
:
λ
b
=
2
:
1
So,
P
divides
A
B
internally in the ratio
1
:
2
while
Q
divides internally in the ratio
2
:
1
. Thus, the coordinates of
P
(
a
,
b
)
and
Q
(
c
,
d
)
are
P
(
a
,
b
)
=
(
1
×
−
3
+
2
×
1
1
+
2
,
1
×
4
+
2
×
−
2
1
+
2
)
⇒
P
(
a
,
b
)
=
(
−
1
3
,
0
)
And,
Q
(
c
,
d
)
=
(
2
×
−
3
+
1
×
1
2
+
1
,
2
×
4
+
1
×
(
−
2
)
2
+
1
)
⇒
Q
(
c
,
d
)
=
(
−
5
3
,
2
)
Hence, the two points of trisection are
(
−
1
3
,
0
)
and
(
−
5
3
,
2
)
REMARK: As
Q
is the midpoint of
B
P
. So, the coordinates of
Q
can also be obtained by using the midpoint formula.
Suggest Corrections
0
Similar questions
Q.
Find the coordinates of the points of trisection of the line segment joining
(
1
,
−
2
)
and
(
−
3
,
4
)
.
Q.
The coordinates of the point(s), which trisect(s) the line segment joining the points
(
1
,
−
2
)
and
(
−
3
,
4
)
,
are
Q.
The line joining the points
(
1
,
−
2
)
and
(
−
3
,
4
)
is trisected. Find the coordinates of the points of trisection.
Q.
The line segment joining the points
(
1
,
−
2
)
and
(
−
3
,
4
)
is trisected at the points
P
and
Q
. Find the coordinates of the point
P
and
Q
.
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
MATHEMATICS
Watch in App
Explore more
Points of Trisection
Standard X Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app