I need help on using midpoints to draw a triangle... here's the question

"the midpoints of the sides of a triangle are L(4,2), M(2,3), AND N(5,4). What are the coordinates of the vertices of the triangle?"

I understand that you find the slope of each side, but what do you do after that? Please help and thanx

1. Let A, B and C denote the vertices of the triangle you are looking for.

2. Draw the triangle LMN.

3. The side of triangle ABC which passes through L must be parallel to MN:

Calculating the slope MN:
Calculating the equation of the line through L:


4. Do just the same with the points M and N. You then have 3 equations of three lines.

5. Calculate the coordinates of the intersection points of these three lines.

Attached Thumbnails

 

3. The side of triangle ABC which passes through L must be parallel to MN:

I dont get how the line passing through L is parallel to MN.
Any explanation?

There is a theorem whos name is (literally translated) "mid parallel in triangles theorem ":

"The connection between 2 midpoints of 2 sides in a triangle is parallel to the third side and has half the length of the third side."

I've used this theorem.

Thnx fo reminding me m8