Question

Find the ratio in which P(-4 , 6) divides the line joining points A(-6, 10) &

B(3 ,-8​

Answer 1

Given: P(-4, 6) divides the line segment joining the points A(-6, 10) and B(3, -8).

To find: The ratio in which it is done so.

Answer:

Let's assume the ratio is k:1

Section formula:

$\tt \bigg(\dfrac{mx_2\ +\ nx_1}{m\ +\ n},\ \dfrac{my_2\ +\ ny_1}{m\ +\ n}\bigg)$

From the given data, we have:

$\tt m\ =\ k\\\\n\ =\ 1\\\\x_1\ =\ -6\\\\x_2\ =\ 3\\\\y_1\ =\ 10\\\\y_2\ =\ -8$

Using them in the formula,

$\tt P(-4, 6)\ =\ \bigg(\dfrac{(k\ \times\ 3)\ +\ (1\ \times\ -6)}{k\ +\ 1},\ \dfrac{(k\ \times\ -8)\ +\ (1\ \times\ 10)}{k\ +\ 1}\bigg)\\\\\\P(-4, 6)\ =\ \bigg(\dfrac{3k\ -\ 6}{k\ +\ 1},\ \dfrac{-8k\ +\ 10}{k\ +\ 1}\bigg)$

Equating the x - coordinates [same can be done with the y - coordinates as well.],

$\tt -4\ =\ \dfrac{3k\ -\ 6}{k\ +\ 1}\\\\\\-4k\ -\ 4\ =\ 3k\ -\ 6\\\\\\6\ -\ 4\ =\ 3k\ +\ 4k\\\\\\2\ =\ 7k\\\\\\\dfrac{2}{7}\ =\ k$

Therefore, the ratio is 2:7.

P(-4, 6) divides the line segment joining the points A(-6, 10) and B(3, -8) in the ratio 2:7.