find the coordinates of the points of trisection of line segment joining the points A(2,-2) and B(-7,4)

To find the trisection points of a line segment, we divide the line into three equal parts. Let's denote the trisection points as P and Q.

The coordinates of point P, which divides the line segment AB in the ratio 1:2, can be found using the section formula:

P(x1, y1) = [(m1x2 + m2x1) / (m1 + m2), (m1y2 + m2y1) / (m1 + m2)]

Here, A(x1, y1) = (2, -2) and B(x2, y2) = (-7, 4), and the ratio m1:m2 = 1:2.

Substituting these values into the formula, we get:

P = [(1*(-7) + 22) / (1 + 2), (14 + 2*(-2)) / (1 + 2)] P = [-3, 0]

Similarly, the coordinates of point Q, which divides the line segment AB in the ratio 2:1, can be found:

Q(x1, y1) = [(m1x2 + m2x1) / (m1 + m2), (m1y2 + m2y1) / (m1 + m2)]

Here, the ratio m1:m2 = 2:1.

Substituting these values into the formula, we get:

Q = [(2*(-7) + 12) / (2 + 1), (24 + 1*(-2)) / (2 + 1)] Q = [-4, 2]

So, the coordinates of the trisection points of the line segment AB are P(-3, 0) and Q(-4, 2).