Question 397985: how do i do the following problem?
Points D(2,4), E(3,2)and F(4,5) are the midpoints od the sides AC, AB, and BC, respectively, in triangle ABC. Find the coordinates of the veticies of the triangle using systems of equations.
Answer by solver91311(24713)   (Show Source):
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Use the fact that a line through two of the midpoints of the sides of a triangle is parallel to the third side of the triangle.
Hence the line containing the segment DE is parallel to the line containing the segment BC. Use the slope formula to calculate the slope of the line containing the segment DE:
Use the fact that the slopes of parallel lines are equal, i.e.,  , the fact that the line containing the segment BC contains the point F, and the point-slope form of an equation of a line to write an equation of the line containing the segment BC:
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Then put it in Standard Form:
In a similar fashion, determine the slope of the line containing the segment FE so that you can write the equation of the line containing the segment AC, namely:
Now solve the system:
which is perforce a consistent/independent system. The single ordered pair element of the solution set will be the coordinates of the point of intersection of the lines containing segments BC and AC, namely the vertex C of the triangle.
Similarly, determine the standard form equation of the line containing segment AB. That equation plus each of the others already developed will form two additional consistent and independent systems the solution sets of which are the coordinates of points A and B.
John
My calculator said it, I believe it, that settles it
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