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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.

 Aug 27, 2018
 #1
avatar+3994 
+3

Ughhh, answered the wrong question. Find the midpoints of sides: x1+x2/2, x1+x3/2+x2+x3/2, we already know that x1+x2+x3=10, so 10*2=20, but 20/2=10.

 Aug 27, 2018
edited by tertre  Aug 27, 2018
 #2
avatar+98141 
+4

Let  the  x coordinates  of the vertices be   x1, x2 and x3

 

And we know that  x1  + x2  + x3  = 10

 

And the   x coordinates of the midpoints of the sides  are

( x1 + x2 ) / 2     =  x1 /2 +  x /2    

(x2 + x3)/2  =     x2 / 2  +  x3 /2

(x1 + x3) / 2  =    x1 /2  + x3/2

 

Summing these, we get

 

(x 1/ 2) *2   +  ( x2 / 2) * 2   +  (x3 /2) *2  =

 

x1   +  x2  +  x3     =      10

 

 

cool cool cool

 Aug 27, 2018
edited by CPhill  Aug 27, 2018
edited by CPhill  Aug 27, 2018
edited by CPhill  Aug 27, 2018

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