Question

Find the point that divides the line joining $A(2,4)$ and $B(6,8)$ in the ratio $a:1$.

• A. ($\frac{6a+2}{a+1},\frac{8a+4}{a+1}$)
• B. ($\frac{6a+4}{a},\frac{8a+2}{a}$)
• C. ($\frac{6a+4}{a+1},\frac{8a+2}{a+1}$)
• D. ($\frac{6a}{a+1},\frac{8a}{a+1}$)

Answer 1

The correct option is A

($\frac{6a+2}{a+1},\frac{8a+4}{a+1}$)

We shall find the coordinates of a point dividing the line joining two points $A(2,4)$ and $B(6,8)$ in the ratio $a:1$.

Let the coordinates of this point be $(x,y)$.

Then the part of the line from $(2,4)$ to $(x,y)$ is $\frac{a}{a+1}$(which we call as $\frac{p}{w}$) of the whole line.

Then, by section formula, we have,

$x=x_1+\frac{p}{w}(x_2-x_1)$ = $2+\frac{a}{a+1}(6-2)$ = $\frac{6a+2}{a+1}$

$y=y_1+\frac{p}{w}\left(y_2-y_1\right)$ = $4+\frac{a}{a+1}(8-4)$ = $\frac{8a+4}{a+1}$

$\therefore$ The point is ($\frac{6a+2}{a+1},\frac{8a+4}{a+1}$).