SOLUTION: The points L(4,3), M(7,4), and N(5,2) are the midpoints of the sides triangle TRI. Use this information to find the coordinates of triangle TRI. How do I solve this?

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Question 1009014: The points L(4,3), M(7,4), and N(5,2) are the midpoints of the sides triangle TRI. Use this information to find the coordinates of triangle TRI. How do I solve this?
Found 2 solutions by fractalier, Edwin McCravy:
Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
When you connect the midpoints of the sides of a triangle they form another triangle with sides parallel AND half as long as the original...it is called a similar triangle to the original...
The slopes of the lines that connect these points are the slopes of the sides of the triangle...their lengths are half that of the original...
Draw a triangle and connect the midpoints...you'll see what I mean...
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
We are given the coordinates of points L,M,N and we want to find the 
coordinates of the point T,R,I:



The little black triangle is similar to the big green triangle, and the big
triangle's sides are exactly twice as long as the corresponding sides of the
small black triangle.  The corresponding sides are parallel. 

Strategy (it's a lot of work!)

1. Use the slope formula 



to find the slopes of each of the three sides of the
little black triangle.  Remember that the sides of the little black
triangle are parallel to the corresponding sides of the big green 
triangle.

2. Use the point slope formula 



to find the equations of each of the 
three sides of the big green triangle.

3. Solve each of the systems of pairs of the equations found in step 2,
by substitution or elimination.  The coordinates obtained will be the
coordinates of points T, R,and I.

If you have any trouble, let me know in the thank-you note form below
and I'll get back to you by email.  (BTW I do this for fun.  I don't
charge a cent.)

Edwin
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