​Find the coordinates of the point which will divide the line joining the point (2, 4) and (7, 9) internally in the ratio 1 : 2​

Correct option is B

Given:

Points: (2, 4) and (7, 9)

Ratio: 1 : 2

Formula used:

If a point P(x, y) divides the line segment joining two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ internally in the ratio m:n, then the coordinates of P are given by:

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

Solution:

Applying the section formula;

​$$P\left( \frac{1 \times 7 + 2 \times 2}{1+2}, \frac{1 \times 9 + 2 \times 4}{1+2} \right)$$

​​$$P\left( \frac{7 + 4}{3}, \frac{9 + 8}{3} \right)$$

​​$$P\left( \frac{11}{3}, \frac{17}{3} \right)$$ 

The coordinates of the point that will divide the line joining the points (2, 4) and (7, 9) internally in the ratio 1:2 are $$\left (\frac{11}{3}, \frac{17}{3}\right)$$​​

​