if the points A(1,2),O(0,0),C(a,b) are collinear , then what is the ralation netween a and b

To determine the relation between a and b when the points A(1,2), O(0,0), and C(a,b) are collinear, we can use the concept of slope.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, we have the points A(1,2) and O(0,0) on the line. So, the slope of the line passing through these two points is:

slope = (0 - 2) / (0 - 1) = -2 / -1 = 2

Now, let's consider the point C(a,b) on the same line. The slope of the line passing through O(0,0) and C(a,b) should be equal to the slope we calculated earlier, which is 2.

So, we can write the equation:

slope = (b - 0) / (a - 0) = 2

Simplifying this equation, we get:

b / a = 2

Therefore, the relation between a and b when the points A(1,2), O(0,0), and C(a,b) are collinear is b = 2a.