Line ab is a directed segment with endpoints a(2,2) and b(14,14). in two or more complete sentences, explain how you would verify that point x, with a coordinate of (6,6), divides line ab in a 1: 2 ratio?

It is not recommended that points be marked with X, let's marked with C(6,6)=(Xc,Yc)

The coordinates of the point C(Xc,Yc) which belongs to the line AB and divides line AB in a ratio m : n = 1 : 2 or m/n=1/2 are get it with following formula

Xc=(Xa+(m/n)Xb) / (1+(m/n)) and Yc=(Ya+(m/n)Yb) / (1+(m/n))

We have A(2,2)=(Xa,Ya) and B(14,14)=(Xb,Yb)

When we replace given coordinates we get

Xc=(2+(1/2)*14) / (1+(1/2)) = (2+7) /(3/2) = 9/(3/2) = (9*2)/3 = 3*2 =6 => Xc=6

Yc=(2+(1/2)*14) / (1+(1/2)) = (2+7) / (3/2) = 9/(3/2) = (9*2)/3 = 3*2 =6 => Yc=6

C(Xc,Yc)=(6,6)

Good luck!!!