Explanation

Using the section formula for internal division: If a point $(x, y)$ divides the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ in the ratio $m:n$, then: $x = \frac{mx_2 + nx_1}{m+n}$ and $y = \frac{my_2 + ny_1}{m+n}$ Given: A(4, 2), B(2, 6), C(9, y), ratio $m:n = 2:5$. For the y-coordinate: $2 = \frac{2(y) + 5(6)}{2+5}$ $2 = \frac{2y + 30}{7}$ $14 = 2y + 30$ $14 - 30 = 2y$ $-16 = 2y$ $y = -8$…