Question

In what ratio does the point (1, a) divide the join of (–1, 4) and (4, –1)? Also, find the value of a.

Answer 1

Let the point P (1, a) divides the line segment AB in the ratio k : 1.

Using section formula, we have:

${\displaystyle 1=\frac{4k-1}{k+1}}$

${\displaystyle \Rightarrow k+1=4k-1}$

${\displaystyle \Rightarrow 2=3k}$

${\displaystyle \Rightarrow k=\frac{2}{3}}$  ...(1)

${\displaystyle \Rightarrow a=\frac{-k+4}{k+1}}$

${\displaystyle \Rightarrow a=\frac{-\frac{2}{3}+4}{\frac{2}{3}+1}}$   ...(From 1)

${\displaystyle \Rightarrow a=\frac{10}{5}=2}$

Hence, the required is 2 : 3 and the value of a is 2.