Point A (4, 2) divides segment BC in the ratio 2 : 5. Coordinates of B and C are (2, 6), (9, y) respectively. Find the value of y.

-8

The correct answer is Option (4) → -8

Using the section formula (internal division):

Point A(x, y) dividing $B(x_1, y_1)$ and $C(x_2, y_2)$ in the ratio $m:n$ is given by

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

Given:

• A(4, 2)
• B(2, 6)
• C(9, y)
• Ratio = 2:5

Check x-coordinate:

$4 = \frac{2(9) + 5(2)}{7} = \frac{18 + 10}{7} = \frac{28}{7} = 4$

Use y-coordinate:

$2 = \frac{2(y) + 5(6)}{7}$

$2 = \frac{2y + 30}{7}$

$2y + 30 = 14$

$2y=−16$

$y = -8$