SOLUTION: The sum of the x-coordinates of the vertices of a triangle in the Cartesian plane equals 10. Find the sum of the x-coordinates of the midpoints of the sides of the triangle.

Algebra ->  Coordinate-system -> SOLUTION: The sum of the x-coordinates of the vertices of a triangle in the Cartesian plane equals 10. Find the sum of the x-coordinates of the midpoints of the sides of the triangle.      Log On


   

Question 1111188: The sum of the x-coordinates of the vertices of a triangle in the Cartesian plane equals 10. Find the sum of the x-coordinates of the midpoints of the sides of the triangle.
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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Let  a, b and c  be x-coordinates of the three vertices.


You are given that  a + b + c = 10.


Midpoints have x-coordinates 0.5(a+b), 0.5(a+c) and 0.5(b+c).


When you add them, you will get


0.5(a+b) + 0.5(a+c) + 0.5(b+c) = a + b + c = 10,


i.e. the same 10 units as your answer.