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.
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