A point P divides the line internally connecting the points (5,0) and (0,4) in the ratio 2 : 3. Find the x coordinate of point P.

According to the question, point P divides the line segment in a ratio of 2 : 3 internally.

Let coordinates of point P let (x, y).

If a point divides a line segment internally with m: n then by section formula: 

$\mathrm{x}=\frac{{\mathrm{mx}}_2+{\mathrm{nx}}_1}{\mathrm{m}+\mathrm{n}} , \mathrm{y}=\frac{{\mathrm{my}}_2+{\mathrm{ny}}_1}{\mathrm{m}+\mathrm{n}}$

Given points: (5,0) and (0,4)

Here, m = 2, n = 3, x₁ = 5, y₁ = 0, x₂ = 0 and y₂ = 4.

Hence, x co-ordinates of P:

$\Rightarrow \mathrm{x}=\frac{2\times 0+3\times 5}{3+2}$

$\Rightarrow \mathrm{x}=\frac{0+15}{5}$

$\Rightarrow \mathrm{x}=\frac{15}{5}= 3$

Thus, the x coordinate of point P = 3