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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
P:
Midpoint Coordinates
x=%280-2%29%2F2=-1
y=%281-3%29%2F2=-2%2F2=-1
P(-1,2)

Q:
Midpoint Coordinates
x=%280%2B2%29%2F2=1
y=%281-1%29%2F2=0
Q(1,0)

Show that PQ has the same slope as AC (meaning that they are parallel).
%282-0%29%2F%28-1-1%29=%281-%28-1%29%29%2F%280-2%29
2%2F%28-2%29=2%2F%28-2%29
-1=-1
Both slopes are -1; so segment PQ is parallel to segment AC.

Is PQ=%281%2F2%29BC ?
If this equation is true, then yes. If false, then no.

Answer by ikleyn(52780) About Me  (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.