Find the coordinates of the point which divides the line segment joining the points P(11, 1) and Q(2, 7) internally in the ratio 2:1 and externally in the ratio 3:5.

Here's how to solve question 6:

Given points are $P(11, 1)$ and $Q(2, 7)$.
Let $P = (x_1, y_1) = (11, 1)$ and $Q = (x_2, y_2) = (2, 7)$.

The section formula for a point $(x, y)$ that divides the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ in the ratio $m:n$ is:
For internal division:

$$(x, y) = \left( \frac{nx_1 + mx_2}{m+n}, \frac{ny_1 + my_2}{m+n} \right)$$

For external division:

$$(x, y) = \left( \frac{nx_1 - mx_2}{n-m}, \frac{ny_1 - my_2}{n-m} \right)$$