Solution 1

The basic theorem that two vectors are parallel: If two A and B vectors are parallel (where B is not a zero vector), there is a real number t∈R, so that: a=tb.

In this problem: AB=(2, -2), AC = (A- 1, B- 1).

Because these two vectors are parallel, then:

There is a real number t such that: AC=tAB.

Namely:

(a- 1，b- 1)=t(2，-2)=(2t，-2t)

Get:

a- 1=2t、b- 1=-2t

Add the two together and you get:

(a- 1)+(b- 1)=0

Solution 2

Vector AB=(x 1, y 1) is parallel to vector CD=(x2, y2), then: X 1Y2-X2Y 1 = 0.