Length of the median through A of the
through A (0,0,6) B(0,4,0) and C ( 3,4,5)
are:
Answers
Answer:
Given:-
The triangle of the vertices A(0,0,6) ,B(0,4,0) and (6,0,0).
To find:-
Find the length of the medians of the triangle..?
Solutions:-
Let AD, BE and CF be the medians of the given triangle ABC.
Since AD is the median, D is the mid point of BC.
Therefore,
Coordinates of point = D = (0 + 6 / 2, 4 + 0 / 2, 0 + 0 / 2)
D = (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.
Therefore,
Coordinates of point = E = (0 + 6 / 2, 0 + 0 / 2, 6 + 0 / 2)
E = (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.
Therefore,
Coordinates of point = F = (0 + 0 / 2, 0 + 4 / 2, 6 + 0 / 2)
D = (0, 2, 3)
CF = √(6 - 0)² + (0 - 2)² + (0 - 3)²
= √36 + 4 + 9
= √49
= 7
Hence, the length of the median of ∆ABC are 7, √34 and 7.