Let P and Q be the points of trisection of the line segment joining the points A(2,-6) and B(8,4) such that P is nearer to A. Find the coordinates of P and Q.

Since P and Q are the points of trisection of the line segment joining the points A(2,-6) and B(8,4) such that P is nearer to A. Therefore, P divides the line segment in the ratio 1:2 and Q divides in 2:1 as shown in the figure.

Using section formula,
Coordinates of P = [mx₂ + nx₁/m+n, my₂ + ny₁/m+n] = [1(8) + 2(2)/1+2, 1(4) + 2(-6)/1+2] = [8+4/3, 4-12/3] = [12/3, -8/3] = [4, -8/3]

Coordinates of Q = [2(8) + 1(2)/2+1, 2(4) + 1(-6)/2+1] = [16+2/3, 8-6/3] = [18/3, 2/3] = [6, 2/3]