The points L, M and N are such that LMN is a straight line - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 2

Let the coordinates of N be (x, y).

Using the section formula, the point N divides the line segment LM in the ratio of 2:3, which means:

$x = \frac{3(-3) + 2(4)}{2 + 3}$

Calculating this gives:

$x = \frac{-9 + 8}{5} = \frac{-1}{5}$

For the y-coordinate, we use:

$y = \frac{3(1) + 2(9)}{2 + 3}$

Calculating gives:

$y = \frac{3 + 18}{5} = \frac{21}{5}$

Thus, the coordinates of N are (-1/5, 21/5).