by Mary

(China)

By observing carefully, we can see that if the origin O(0,0) is located on the line AB, the slope of the line segment OA is the same as the slope of the line segment OB. Hence, we can prove this question by showing that the slope of the line OA and OB are the same.

To calculate the slope of a line, we can use the slope formula:

Let's find the slope of the line OA first. To do so, we let:

Substituting the above values into the slope formula, we have:

m =

=

=

=

Similarly, we now find the slope of the line OB. To do so, we let:

Substituting the above values into the slope formula, we have:

m =

=

=

=

=

We can see that the line segment OA and OB have the same slope (m = 1.5). Therefore, we proved that the line AB passes through the origin...