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.

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FirstInTest · Accepted Answer

Correct answer: D. 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:
$2 = \frac{2(y) + 5(6)}{2+5}$
$2 = \frac{2y + 30}{7}$
$14 = 2y + 30$
$14 - 30 = 2y$
$-16 = 2y$
$y = -8$.

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