2 Question 4 (4 points)
Gina wrote the following paragraph to prove that the segment joining the midpoints of two sides of a triangle is parallel to the third side:
Glver: AABC
Prove: The midsegment between sides
AB
and
BC
Is parallel to side AC
Draw AABC on the coordinate plane with point A at the origin (0,0). Let point B have the ordered pair (X1, Yı) and locate point on the x-axis at
0+x 0+y
2
(X2, 0). Point D is the midpoint of AB with coordinates at
by the slope formula. Point E is the midpoint of BC with an ordered
x+x. 0+y
2
pair of
by the slope formula. The slope of DE is found to be through the application of the slope formula:
[oty ory
2 2
0
=0
X + x 0+
Y, -Y 0-0 0
2 2
When the slope formula is applied to AC *-, X-OX,
Its slope is also O. Since
the slope of DE and AC are identical, DE and AC are parallel by the definition of parallel lines.
Which statement corrects the flaw in Gina's proof? (4 points)
0
Оа
Ob
Ос
Od
The coordinates of D and E were found using the Midpoint Formula
Segments DE and AC are parallel by construction
The slope of segments DE and AC is not 0.
The coordinates of D and E were found using the Distance between Two Points Postulate