SOLUTION: A(0,1), B(-2,3) and C(2,-1) are the vertices of a triangle ABC. P and Q are the midpoints of the sides AB and AC. Show that PQ is parallel to BC and, Show that PQ = 1/2 lenght B

Question 988123: A(0,1), B(-2,3) and C(2,-1) are the vertices of a triangle ABC. P and Q are the midpoints of the sides AB and AC.
Show that PQ is parallel to BC and, Show that PQ = 1/2 lenght BC.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
P:
Midpoint Coordinates

P(-1,2)

Q:
Midpoint Coordinates

Q(1,0)

Show that PQ has the same slope as AC (meaning that they are parallel).

Both slopes are ; so segment PQ is parallel to segment AC.

Is ?
If this equation is true, then yes. If false, then no.

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
It is the general (the common) property of a straight line segment connecting midpoints of two sides of a triangle:

The straight line segment connecting midpoints of two sides of a triangle is parallel to the third side and is half of its length.

See the lesson The line segment joining the midpoints of two sides of a triangle in this site.

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