Question

Find the coordinates of the point which divides the line segment joining the points A (-6, 10) and B (3, -8) in the ratio 2:7​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given: The line segment formed by the points A(-6, 10) and B(3, -8) is divided in the ratio 2:7.

To find: The coordinate that divides it.

Answer:

Section formula:

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

From the give data, we have,

$\tt m\ =\ 2\\\\n\ =\ 7\\\\x_1\ =\ -6\\\\x_2\ =\ 3\\\\y_1\ =\ 10\\\\y_2\ =\ -8$

Using them in the formula,

$\tt \Bigg(x,\ y\Bigg)\ =\ \Bigg(\dfrac{(2\ \times\ 3)\ +\ (7\ \times\ -6)}{2\ +\ 7},\ \dfrac{(2\ \times\ -8)\ +\ (7\ \times\ 10)}{2\ +\ 7}\Bigg)\\\\\\\Bigg(x,\ y\Bigg)\ =\ \Bigg(\dfrac{6\ -\ 42}{9},\ \dfrac{-16\ +\ 70}{9}\Bigg)\\\\\\\Bigg(x,\ y\Bigg)\ =\ \Bigg(\dfrac{-36}{9},\ \dfrac{54}{9}\Bigg)\\\\\\\Bigg(x,\ y\Bigg)\ =\ \Bigg(-4,\ 6\Bigg)$

Therefore, the line segment formed by the points A(-6, 10) and B(3, -8) is divided in the ratio 2:7 by the point (-4, 6).