Question

find the coordinates of the point which divide the line segment joining the points A(5,-25) and B(10,-20) in the ratio 1:4​

Answer 1

Given: The line segment joined by the points A(5, -25) and B(10, -20) is divided in the ratio 1:4.

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

Answer:

Section formula:

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

From the given data,

$\tt m\ =\ 1\\\\n\ =\ 4\\\\x_1\ =\ 5\\\\x_2\ =\ 10\\\\y_1\ =\ -25\\\\y_2\ =\ -20$

Using them in the formula,

$\tt \bigg(x,\ y\bigg)\ =\ \bigg(\dfrac{(1\ \times\ 10)\ +\ (4\ \times\ 5)}{1\ +\ 4},\ \dfrac{(1\ \times\ -20)\ +\ (4\ \times\ -25)}{1\ +\ 4}\bigg)\\\\\\\bigg(x,\ y\bigg)\ =\ \bigg(\dfrac{10\ +\ 20}{5},\ \dfrac{-20\ -\ 100}{5}\bigg)\\\\\\\bigg(x,\ y\bigg)\ =\ \bigg(\dfrac{30}{5},\ \dfrac{-120}{5}\bigg)\\\\\\\bigg(x,\ y\bigg)\ =\ \bigg(6,\ -24\bigg)$

Therefore, (6, -24) divides the line segment joining the points A(5, -25) and B(10, -20) in the ratio 1:4.