SOLUTION: the midpoint of the sides of a triangle are L(4,2),M(2,3)andN(5,4).What are the coordinates of the vertices of the triangle,
please help. have a test tomm
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Question 247392: the midpoint of the sides of a triangle are L(4,2),M(2,3)andN(5,4).What are the coordinates of the vertices of the triangle,
please help. have a test tomm
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
A line segment that joins the midpoints of two sides of a triangle is parallel to the third side. So, using two of the given midpoints, you can calculate the slope of the segment that joins the mid-points using the slope formula.
where )
and )
are the given mid-points.
Then, using the slope you just calculated and the third midpoint, you can derive an equation of the line that contains the side of the triangle using the point-slope form of the equation of a line.
 )
where 
is the slope you just calculated and are the coordinates of the third mid-point.
You need to perform the above procedure one more time using a different pair of midpoints. Now you have two equations that form a system of equations. The solution set of the system is the ordered pair representing one vertex of the triangle.
Once you have one vertex, you can use the midpoint formulae to calculate the coordinates of the other two vertices.
and
You know 
and 
because they are givens, and you know 
and 
because they are the known vertex coordinates.
John
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