We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# sum of cartesian

+1
164
2
+814

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

### 2+0 Answers

#1
+4223
+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
+100569
+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

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