One of the two points of trisection of the line segment joining the points A(7, –2) and B(1, –5) which divides the line in the ratio 1 : 2 is :

The trisection points of a line segment are the points that divide the line into three equal parts. However, in this case, we are asked to find the point that divides the line in the ratio 1:2. This means that the point is one third of the way from point A to point B.

The formula to find a point that divides a line segment AB in the ratio m:n is given by:

((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))

where (x1, y1) and (x2, y2) are the coordinates of points A and B respectively.

Here, A(7, -2) and B(1, -5) are the coordinates of points A and B, and m:n is 1:2.

Substituting these values into the formula, we get:

((11 + 27) / (1 + 2), (1*-5 + 2*-2) / (1 + 2))

Solving this, we get:

(5, -3)

So, one of the two points of trisection of the line segment joining the points A(7, –2) and B(1, –5) which divides the line in the ratio 1 : 2 is (5, -3).