Question

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

The equation for the point that divides a line segment joining the points $(x_1,y_1)and(x_2,y_2)$ in the ratio m : n is: $(\frac{(n\times x_1+m\times x_2)}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$


Here, $(x_1,y_1)=(2,1)\text{and}(x_2,y_2)=(6,8)$

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