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 a, b and c
Midpoint x value of a,b coordinates = (a + b)/2
Midpoint x value of b,c coordinates = (b + c)/2
Midpoint x value of a,c coordinates = (a + c) / 2
The sum of the midpoint x values is
[ 2a + 2b + 2c ] / 2 = a + b + c = 10