2. Find the lengths of the medians of the triangle with vertices A (0,0.6). B (0,4,0)
and (6, 0, 0).
Answers
Answer:
Let AD,BE and CF be the medians of the given △ABC.
Since AD is the median, D is the mid-point of BC.
∴ coordinates of point D= (
2
0+6
,
2
4+0
,
2
0+0
)=(3,2,0)
AD=
(0−3)
2
+(0−2)
2
+(6−0)
2
=
9+4+36
=
49
=7
Since BE is the median, E is the mid-point of AC.
∴ coordinates of point E= (
2
0+6
,
2
0+0
,
2
6+0
)=(3,0,3)
BE=
(3−0)
2
+(0−4)
2
+(3−0)
2
=
9+16+9
=
34
Since CF is the median, F is the mid point of AB.
∴ coordinates of point F= (
2
0+0
,
2
0+4
,
2
6+0
)=(0,2,3)
Length of CF=
(6−0)
2
+(0−2)
2
+(0−3)
2
=
36+4+9
=
49
=7
Thus the lengths of the medians of △ABC are 7,
34
and 7 units.
Step-by-step explanation:
Step-by-step explanation:
midpoint of BC=(3,2,0)
median AD=√(0-3)^2+(0-2)^3+(6-0)^2
=√9+4+36=7
midpoint of AC (3,0,3)
median BE=√(3^2+4^2+3^2
=√9+16+9=√34
midpoint of AB(0,2,3)
median CF=√6^2+2^2+3^2
=√36+4+9=7