Solve
Study
Textbooks
Guides
Join / Login
>>
Class 11
>>
Maths
>>
Introduction to Three Dimensional Geometry
>>
Distance between Two Points
>>
Find the lengths of the medians of the t
Question
Find the lengths of the medians of the triangle with vertices
A
(
0
,
0
,
6
)
,
B
(
0
,
4
,
0
)
and
(
6
,
0
,
0
)
.
Medium
Open in App
Solution
Verified by Toppr
Let
A
D
,
B
E
and
C
F
be the medians of the given
△
A
B
C
.
Since
A
D
is the median,
D
is the mid-point of
B
C
.
∴
coordinates of point
D
=
(
2
0
+
6
,
2
4
+
0
,
2
0
+
0
)
=
(
3
,
2
,
0
)
A
D
=
(
0
−
3
)
2
+
(
0
−
2
)
2
+
(
6
−
0
)
2
=
9
+
4
+
3
6
=
4
9
=
7
Since
B
E
is the median,
E
is the mid-point of
A
C
.
∴
coordinates of point
E
=
(
2
0
+
6
,
2
0
+
0
,
2
6
+
0
)
=
(
3
,
0
,
3
)
B
E
=
(
3
−
0
)
2
+
(
0
−
4
)
2
+
(
3
−
0
)
2
=
9
+
1
6
+
9
=
3
4
Since
C
F
is the median,
F
is the mid point of
A
B
.
∴
coordinates of point
F
=
(
2
0
+
0
,
2
0
+
4
,
2
6
+
0
)
=
(
0
,
2
,
3
)
Length of
C
F
=
(
6
−
0
)
2
+
(
0
−
2
)
2
+
(
0
−
3
)
2
=
3
6
+
4
+
9
=
4
9
=
7
Thus the lengths of the medians of
△
A
B
C
are
7
,
3
4
and
7
units.
Solve any question of
Introduction to Three Dimensional Geometry
with:-
Patterns of problems
>
Was this answer helpful?
0
0
Find All solutions for this book
Mathematics
NCERT
Miscellaneous Exercise
Similar questions
The points
(
2
,
3
,
4
)
,
(
−
1
,
−
2
,
1
)
,
(
1
,
2
,
5
)
and
(
4
,
7
,
8
)
are the vertices of a
Medium
View solution
>
If
(
1
,
−
1
,
0
)
,
(
−
2
,
1
,
8
)
and
(
−
1
,
2
,
7
)
are three consecutive vertices of a parallelogram then the fourth vertex is
Medium
View solution
>
The vertices of a triangle are
A
(
0
,
0
)
,
B
(
0
,
2
)
and
C
(
2
,
0
)
. The distance between circumcenter and orthocenter is:
Medium
View solution
>
Find the coordinate of the point
P
where the line through
A
(
3
,
−
4
,
−
5
)
and
B
(
2
,
−
3
,
1
)
crosses the plane passing through three points
L
(
2
,
2
,
1
)
,
M
(
3
,
0
,
1
)
and
N
(
4
,
−
1
,
0
)
. Also, find the ratio in which
P
divides the line segment
A
B
.
Medium
View solution
>
If the orthocentre, circumcentre of a triangle are
(
−
3
,
5
,
2
)
,
(
6
,
2
,
5
)
respectively then the centroid of the triangle is
Medium
View solution
>
View more
More From Chapter
Introduction to Three Dimensional Geometry
View chapter
>
Revise with Concepts
Distance Formula in 3D Geometry
Example
Definitions
Formulaes
Learn with Videos
Distance Formula and Its Use in 3D Geometry
17 mins
Shortcuts & Tips
Common Misconceptions
>
Problem solving tips
>
Important Diagrams
>
Mindmap
>
Memorization tricks
>
Cheatsheets
>
Practice more questions
Easy Questions
94 Qs
>
Medium Questions
374 Qs
>
Hard Questions
73 Qs
>