Math, asked by pranalisawadh, 2 months ago

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

Answered by 16mpickering
1

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:

Answered by amitsharma777222999
0

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

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