Question

If the line x + y = 10, divides the line segment joining A(2,4) and B(6,8) in the ratio a : 1, then, a = .

• A. 1
• B. 2
• C. 3

Answer 1

The correct option is A 1

Let the point, say P(x, y), divide the line AB in the ratio a : 1. The coordinates of the point that divides a line in the ratio m : n is,$(\frac{n{x}_1+m{x}_2}{m+n},\frac{n{y}_1+m{y}_2}{m+n})$

where $(x_1,y_1)\text{and}(x_2,y_2)$ are the coordinates of the endpoints of the line segment.
Applying the formula, we get $(\frac{1\times 2+a\times 6}{a+1},\frac{1\times 4+a\times 8}{a+1})$

Also,this point lies on the line x + y = 10, so substitute the points in the equation of the line.

$\Rightarrow \frac{1\times 2+a\times 6}{a+1}+\frac{1\times 4+a\times 8}{a+1}=10$

$\Rightarrow 6a+2+8a+4=10(a+1)$

$\Rightarrow 14a+6=10a+10$
$\Rightarrow 4a=4$
$\Rightarrow a=1$