Let given points be A(3, -4) and B(1, 2) , which is trisected at points P(p, -2) and Q(\(\frac{5}3\), q).
By section formula,
x = \(\frac{mx_2+nx_1}{m+n}\), y = \(\frac{my_2+ny_1}{m+n}\)
As point P divides the line in 1:2 and Q divides the line in 2:1.
For point P(p, -2)of AB, where m = 1 and n = 2,
p = \(\frac{1\times1+3\times2}{1+2}\), -2 = \(\frac{2\times1+2\times(-4)}{1+2}\)
Solving for p,
p = \(\frac{7}3\)
For point Q(5/3, q) of AB, where m = 2 and n = 1,
\(\frac{5}3\) = \(\frac{2\times1+1\times3}{2+1}\),q = \(\frac{2\times2+1\times(-4)}{2+1}\)
Solving for q,
q = \(\frac{4-4}3\)
∴ q = 0Hence, the value of p and q are \(\frac{7}3\) and 0 respectively.