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.

mathtoo Aug 27, 2018

#2**+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

CPhill Aug 27, 2018