Question

Find the ratio in which the point R ( 1, 5) divides the line segment joining the points S (-2, -1) and T (5, 13). 

Answer 1

Let R divides the line segment ST in the ratio k : 1. Coordinates of R 

R ( x, y) = R ( 1, 5) 

R `((5"k" - 2)/("k" + 1) , (13 "k" - 1)/("k" + 1))` = R (1 , 5)

`(5"k" - 2)/("k" +1) = 1`

5 k - 2 = k + 1

4 k = 3

k = `3/4`

Hence, required ratiois  k :1 = 3 : 4.