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prove this qsn plzz and fast​

Prove This Qsn Plzz And Fast class=

Sagot :

Step-by-step explanation:

Let use the first of the medians. Medians AX.

Median AX is the midpoint of BC so our median is

[tex] \frac{1}{2} (b + c) - a[/tex]

Let use the second median.

Median BY is the midpoint of AC so our median is

[tex] \frac{1}{2} (a + c) - b[/tex]

Let use the final median.

Median CZ is the midpoint of AB so our median is

[tex] \frac{1}{2} (a + b) - c[/tex]

Now add all them up

[tex] \frac{1}{2} (b + c ) - a + \frac{1}{2} (a + c) - b + \frac{1}{2} (a + b) - c[/tex]

[tex] \frac{1}{2} b + \frac{1}{2} c - a + \frac{1}{2} a + \frac{1}{2} c - b + \frac{1}{2}a + \frac{1}{2} b - c[/tex]

Add like terms.

[tex] \frac{1}{2} b + \frac{1}{2} b - b = 0[/tex]

[tex] \frac{1}{2} a + \frac{1}{2} a - a = 0[/tex]

[tex] \frac{1}{2} c + \frac{1}{2} c - c = 0[/tex]

[tex]0 + 0 + 0 = 0[/tex]

So

AX+BY+CZ=0

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