Answer :

Given: vertices of triangle ABC i.e. A (1, 8), B (–2, 4), C (8, –5)

M and N are mid – points of AB and AC.

__Finding co–ordinates of M and N:__

We know that,

M is the mid–point of AB

x_{1} = 1, x_{2} = –2

y_{1} = 8, y_{2} = 4

Mid–point formula M (x, y)

Mid–point of AB

N is the mid–point of AC

x_{1} = 1, x_{2} = 8

y_{1} = 8, y_{2} = –5

Mid–point of AC

__Slope of MN:__

Slope of line passing through (x_{1}, y_{1}) and (x_{2}, y_{2}) is

__Verification of MN and BC are parallel:__

If MN and BC are parallel, then their slopes must be equal.

__Slope of BC:__

B (–2, 4) and C (8, –5)

Slope of BC

∴ Slope of MN = Slope of BC =

Hence, MN is parallel to BC.

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