Q. 125.0( 1 Vote )

# The vertices of Δ

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

x1 = 1, x2 = –2

y1 = 8, y2 = 4

Mid–point formula M (x, y)

Mid–point of AB

N is the mid–point of AC

x1 = 1, x2 = 8

y1 = 8, y2 = –5

Mid–point of AC

Slope of MN:

Slope of line passing through (x1, y1) and (x2, y2) 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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