Introduction:
The problem requires finding the coordinates of the points of trisection on the line segment joining the points A(8,3) and B(11,5). Trisection means dividing a line segment into three equal parts. To find the coordinates of the points of trisection, we can use the concept of section formula.

Section Formula:
The section formula helps in finding the coordinates of a point that divides a line segment into a given ratio. It states that if a line segment AB is divided by a point P(x,y) in the ratio m:n, then the coordinates of point P can be found using the following formula:
x = (mx1 + nx2) / (m + n)
y = (my1 + ny2) / (m + n)

Given Points:
A(8,3) and B(11,5)

Finding the First Point of Trisection:
To find the coordinates of the first point of trisection, we need to divide the line segment AB in the ratio 1:2.
Using the section formula:
x = (1*8 + 2*11) / (1 + 2) = (8 + 22) / 3 = 30 / 3 = 10
y = (1*3 + 2*5) / (1 + 2) = (3 + 10) / 3 = 13 / 3

Therefore, the coordinates of the first point of trisection are (10, 13/3).

Finding the Second Point of Trisection:
To find the coordinates of the second point of trisection, we need to divide the line segment AB in the ratio 2:1.
Using the section formula:
x = (2*8 + 1*11) / (2 + 1) = (16 + 11) / 3 = 27 / 3 = 9
y = (2*3 + 1*5) / (2 + 1) = (6 + 5) / 3 = 11 / 3

Therefore, the coordinates of the second point of trisection are (9, 11/3).

Conclusion:
The coordinates of the points of trisection on the line segment joining the points A(8,3) and B(11,5) are (10, 13/3) and (9, 11/3). These points divide the line segment into three equal parts.