For ΔABC with A(–5, –4), B(3, –2), and C(–1, 6), M is the midpoint of AB
and N is the midpoint of
BC
. Show that MN = 1/2 AC. Provide your complete solutions and proofs in your paper homework and enter the numeric answers online.

The proposition is true, as and satisfies the given expression ().

Step-by-step explanation:

Vertices of the triangle ABC are located in , and , respectively. By definition of midpoint, we get that M and N are located in the following coordinates:

(Eq. 1)

(Eq. 2)

Then, the relative vectors between A and C, as well as M and N are, respectively:

(Eq. 3)

(Eq. 4)

By getting back into (Eq. 3), we find the following the result after some algebraic handling:

Which proofs the given affirmation.

could you provide figure.