Find the ratio which the point (4,2) divides the line joining the points (2,-4) and (8,14).

Question

asked Sep 13, 2023 109k views

1 Answer

Jevaun · Answer 1 · 2023-09-19T05:45:35+0000

Given:

The point (4, 2) divides the line joining the points (2, -4) and (8, 14).

To find: The ratio

Explanation:

Let the ratio be,

Using the section formula,

$P=\lparen(mx_2+nx_(1,))/(m+n),(my_2+ny_1)/(m+n))$

Here, we have

$\begin{gathered} m=k,n=1 \\ x_1=2,y_1=-4 \\ x_2=8,y_2=14 \end{gathered}$

On substitution we get,

$(4,2)=\lparen(8k+2)/(k+1),(14k+4)/(k+1))$

Equating the coordinates we get,

$\begin{gathered} 4=(8k+2)/(k+1) \\ 4\left(k+1\right)=8k+2 \\ 4k+4=8k+2 \\ 4k=2 \\ k=(1)/(2) \end{gathered}$

Since,

$\begin{gathered} k=(1)/(2) \\ \therefore m:n=(1)/(2):1 \\ m:n=1:2 \end{gathered}$

Hence, the ratio in which the point (4, 2) divides the line joining the points (2, -4) and (8, 14) is 1: 2.

Final answer: The ratio is,