Question

Prove this qsn plzz and fast​

Answer 1

Explanation:

Let use the first of the medians. Medians AX.

Median AX is the midpoint of BC so our median is

`(1)/(2) (b + c) - a`

Let use the second median.

Median BY is the midpoint of AC so our median is

`(1)/(2) (a + c) - b`

Let use the final median.

Median CZ is the midpoint of AB so our median is

`(1)/(2) (a + b) - c`

Now add all them up

`(1)/(2) (b + c ) - a + (1)/(2) (a + c) - b + (1)/(2) (a + b) - c`

`(1)/(2) b + (1)/(2) c - a + (1)/(2) a + (1)/(2) c - b + (1)/(2)a + (1)/(2) b - c`

Add like terms.

`(1)/(2) b + (1)/(2) b - b = 0`

`(1)/(2) a + (1)/(2) a - a = 0`

`(1)/(2) c + (1)/(2) c - c = 0`

`0 + 0 + 0 = 0`

So

AX+BY+CZ=0