Final answer:
To verify if points A, B, and C are collinear, we calculated the slopes of segments AB and BC, finding both to be 3. This indicates the points are already collinear, so no value of 'a' is required.
Step-by-step explanation:
To determine if points A(1,1), B(2,4), and C(3,7) are collinear, we can use the concept of the slope of a line in a coordinate plane. The slope between two points (x1,y1) and (x2,y2) is calculated as (y2 - y1) / (x2 - x1). If all three points are on the same line, the slope between A and B should be equal to the slope between B and C.
First, let's find the slope of the line segment AB:
Slope of AB = (4 - 1) / (2 - 1) = 3 / 1 = 3
Now, let's find the slope of the line segment BC:
Slope of BC = (7 - 4) / (3 - 2) = 3 / 1 = 3
Since the slopes are equal, the points A, B, and C are indeed collinear. Therefore, there is no need to find a specific value of 'a' to make the points collinear, as they already are.