Find the coordinates of the point which divides the line segment joining the points (2, – 3) and (2, 4) in the ratio 2: 1 internally.

Given,

(2, - 3) = (x_{1}, y_{1})

and

(2, 4) = (x_{2}, y_{2})

Ratio 2:1 so, m = 2 and n = 1
The coordinates of the point (x,y) which divides the line segment joining the points (

x_{1}, y_{1}

) and (

x_{2}, y_{2}

) , internally in the ratio m:n are,

(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})

.
So,

\Rightarrow (x, y) = (\frac{[2 (2) - 1 (2)]}{2 - 1}, \frac{[2 (4) - 1 (- 3)]}{2 - 1})

\Rightarrow (x, y) = (\frac{4 - 2}{1}, \frac{8 + 3}{1})

\Rightarrow (x, y) = (2, 11)

Therefore,

(2, 11)

is the required point.
Hence, option 1 is correct.

Find the coordinates of the point which divides the line segment joining the points $(2, - 3)$ and $(2, 4)$ in the ratio $2 : 1$ internally.