Question

The line x + y = 10 divides line segment AB in the ratio a : 1. Find the value of a.

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• A. 3
• B. 2
• C. 1
• D. $\frac{1}{2}$

Answer 1

The correct option is C

1

The point, say P(x, y), divides the line AB into the ratio a:1.

The coordinates of the point that divides a line internally in the ratio m:n are

$(\frac{n{x}_1+m{x}_2}{m+n},\frac{n{y}_1+m{y}_2}{m+n})$ where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of the endpoints of the line segment.

Applying the formula, we get
$(x,y)=(\frac{a\times 6+1\times 2}{a+1},\frac{a\times 8+1\times 4}{a+1})$

It is given that this point lies on the line represented by the equation x + y = 10, so the point will satisfy the equation.

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

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