Question

The ratio in which the point (m, −6) divides the line segment joining the points (−1, −3), and (9, −8) is ______.

Options

• 3 : 2

• 2 : 3

• 3 : 4

• 4 : 3

Answer 1

The ratio in which the point (m, −6) divides the line segment joining the points (−1, −3), and (9, −8) is 3 : 2.

Explanation:

Let the ratio be k : 1 (AP : PB)

Using the section formula for y:

−6 = `(k(−8) + (−3)) / (k + 1)`

−6(k + 1) = −8k − 3

−6k − 6 = −8k − 3

2k = 3

∴ k = `3/2`

Therefore, the ratio is 3 : 2.