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.

Given: ∆ABC

Prove: The midsegment between sides and is parallel to side .

Draw ∆ABC on the coordinate plane with point A at the origin (0, 0). Let point B have the ordered pair (x1, y1) and locate point C on the x-axis at (x2, 0). Point D is the midpoint of with coordinates at by the slope formula. Point E is the midpoint of with an ordered pair of by the slope formula. The slope of is found to be 0 through the application of the slope formula

Question

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.
 
Given: ∆ABC
 
Prove: The midsegment between sides and is parallel to side .
 
Draw ∆ABC on the coordinate plane with point A at the origin (0, 0). Let point B have the ordered pair (x1, y1) and locate point C on the x-axis at (x2, 0). Point D is the midpoint of with coordinates at by the slope formula. Point E is the midpoint of with an ordered pair of by the slope formula. The slope of is found to be 0 through the application of the slope formula

anonymous · Answer

When the slope formula is applied to , its slope is also 0. Since the slope of and are identical, and are parallel by the definition of parallel lines.
 
Which statement corrects the flaw in Gina's proof? 

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

anonymous · Answer

This is the entire thing with the equations. Just to help.

mertsj · Answer

I'm just wondering why one would find the midpoint with the slope formula rather than using the midpoint formula.

anonymous · Answer

The entire thing is just confusing to me. I'm not good at proofs at all.

mertsj · Answer

Does it seem sensible to you to say that you would find a midpoint using the slope formula?   Why wouldn't you find the slope using the slope formula and use the midpoint formula to find the midpoint????

anonymous · Answer

I don't know, I haven't worked with these in a long time. It does seem best to use slope formula for finding slope, and midpoint formula for midpoint, but I don't know any other ways.

mertsj · Answer

Well, of course.  The midpoint formula is for finding the midpoint and the slope formula is for finding the slope.  Do you think then, that the proof is wrong when it says to use the slope formula to find the midpoint?

mertsj · Answer

And if it is wrong to say that, what would correct that error?

anonymous · Answer

Using the Midpoint Formula? Which would be A?

mertsj · Answer

yes

anonymous · Answer

Thanks :)