Division of a Line in Given Ratio
In this problem, we are given a line segment joining the points (2,1) and another point whose ordinates divide the line segment in the ratio 3:2. Let's denote the coordinates of the point dividing the line segment as (x, y).

Understanding the Ratio
When a line segment is divided by a point in a specific ratio, it means that the ratio of the distances of the point from the two endpoints of the line segment is equal to the given ratio. In this case, the ratio is 3:2.

Using the Section Formula
To find the coordinates of the point dividing the line segment in the ratio 3:2, we can use the section formula. According to the section formula, the coordinates of the point (x, y) dividing the line segment joining the points (x1, y1) and (x2, y2) internally in the ratio m:n are given by:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
In this case, the coordinates of the points are (2, 1) and (x, y) and the ratio is 3:2.

Calculating the Coordinates
Using the section formula, we can calculate the coordinates of the point (x, y) that divides the line segment joining (2, 1) in the ratio 3:2.
x = (3*2 + 2*2) / (3 + 2) = (6 + 4) / 5 = 10 / 5 = 2
y = (3*1 + 2*1) / (3 + 2) = (3 + 2) / 5 = 5 / 5 = 1
Therefore, the coordinates of the point that divides the line segment joining (2, 1) in the ratio 3:2 are (2, 1).