Question

Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.

Answer 1

The end points of AB are  A(-1, 7) and B (4, -3) 

Therefore `(x_1 = -1, y_1 = 7) and (x_2 = 4, y_2 = -3 )`

Also , m = 2 and n = 3

Let the required point be P (x, y). 

By section formula, we get

`x= (("m"x_2 + "n"x_1))/(("m"+"n")) ,   "y" = (("my"_2+"ny"_1))/(("m"+"n"))`

`⇒ x = ({ 2 xx 4 +3 xx (-1) })/(2+3) ,  "y"= ({2 xx (-3) + 3 xx 7})/(2+3)`

`⇒  x = (8-3) /5,  "y" = (-6+21)/5`

`⇒  x = 5/5,  "y" = 15/5`

Therefore, x = 1 and y = 3

Hence, the coordinates of the required point are (1, 3).