The vertices of ΔABC are A (1, 8), B (–2, 4), C (8, –5). If M and N are the midpoints of AB and AC respectively, find the slope of MN and hence verify that MN is parallel to BC.

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.