Question

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

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

Answer 1

The correct option is B

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

The coordinates of the point that divides a line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m : n are

$(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

Let the required point be (a, b).

Here, (a, b) divides the line AB in the ratio a : 1.

$\Rightarrow (a,b)=(\frac{1\times 2+a\times 6}{a+1},\frac{1\times 4+a\times 8}{a+1})$

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