Question

AB is divided in the ratio a:1 by a point which lies on the line x + y = 10. Find the value of a.

• A. 3
• B. 2
• C. 1
• D. 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 equation for the point that divides a line in the ratio m : n is ,

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

Where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of the line. Applying the formula, we get

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

This point lies on the line x + y = 10, so substitute the points in the equation for the line

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

6a + 2 + 8a + 4 = 10(a+1)
4a = 4
a = 1